# Riddler - Solutions to Castles Puzzle: castle-solutions.csv

Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub · About: simonw/fivethirtyeight-datasette

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Link | rowid ▼ | Castle 1 | Castle 2 | Castle 3 | Castle 4 | Castle 5 | Castle 6 | Castle 7 | Castle 8 | Castle 9 | Castle 10 | Why did you choose your troop deployment? |
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1 | 1 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | because, I am number one! |

2 | 2 | 52 | 2 | 2 | 2 | 2 | 2 | 2 | 12 | 12 | 12 | I need to win at least 4 castles to win the game. Any combination of 7 castles wins the game. I assume that the border cases of trying to win 1-7 or 1 and 8-10 will be popular. If possible, I should like to be able to beat either strategy. One way to do that would be to play minimally on all numbers except for 1. Then I take the ones they don't want, but I also steal castle 1, which is less sought after. Of course, I lose to the "10s all around" strategy, which I imagine will also be popular. Notice that the key is not beating a randomly generated opponent, but beating the most opponents, which means I want to be able to beat the most popular strategies. Hmm. The method I've devised will beat "10s all around" and has a shot at beating folks who go all in on another strategy. I expect to get beaten a lot, though, by folks who pick a different set of castles they want to win. Oh well. I've already spent too long on this. If nothing else, I've given you another weird data point! :) |

3 | 3 | 26 | 26 | 26 | 16 | 1 | 1 | 1 | 1 | 1 | 1 | The top 3 are necessary for a majority and the 4th is also needed. The rest are filled in case my opponent leaves them empty. |

4 | 4 | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | The total points up for grabs is 55, and to win the war I need 28 points. I want to get 28 points by using the least number of castles, so I can put more soldiers in each castle and increase my odds of winning that castle. I can earn 28 points by winning castles 1, 8, 9, and 10. So I will put 25 soldiers each in castles 1, 8, 9, and 10 to maximize my odds of winning each of those castles simultaneously. |

5 | 5 | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | Submission #4. A variation of my third submission. Equally divided among just enough points to win. (Not convinced this will win either). |

6 | 6 | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | There are 55 points up for grabs, so 28 are needed to win. Winning castles 1,8,9,10 are the fewest number of castles needed reach 28 points. Castle 1 is as important as castle 10 for getting to 28 points. |

7 | 7 | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | Since there are 55 available points, I only need to win 27.5 or more points to win any given battle. By maximizing my soldiers in the four castles that are worth 28 points combined, I maximize my chances of beating more evenly distributed enemies. |

8 | 8 | 23 | 1 | 1 | 1 | 1 | 2 | 2 | 23 | 23 | 23 | The ones and twos are mostly to pick up any undefended castles, while I hope to grab the highest castles to get me over 27.5. Have to admit I don't know much game theory, so it's mostly just a guess. |

9 | 9 | 21 | 18 | 15 | 13 | 11 | 9 | 6 | 4 | 2 | 1 | On average 1.81 soldiers per point, with some slight weighting to the top castles and unweighting the lower castles. |

10 | 10 | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 26 | 26 | 27 | If you were to win castles 10, 9, 8, and 1 each time, you would win every matchup. I put all of my soldiers on those castles, with a few extra on the more valuable castles to beat out anyone with the same strategy |

11 | 11 | 20 | 12 | 13 | 13 | 14 | 14 | 14 | 0 | 0 | 0 | Get to 28 by conquering the smallest towers |

12 | 12 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 30 | it put high power making it easy to win the castles with troops. |

13 | 13 | 19 | 17 | 15 | 13 | 11 | 9 | 7 | 5 | 3 | 1 | ? |

14 | 14 | 19 | 1 | 1 | 1 | 1 | 1 | 1 | 25 | 25 | 25 | need 28 to win |

15 | 15 | 19 | 1 | 1 | 1 | 1 | 1 | 1 | 25 | 25 | 25 | The total number of points is 55 so you need 28 points to win the war. The smallest combination of castles to win 28 points is 10,9,8,1 so to maximize your chances you should just split your army by 25 soldier each. But this won't work because the other castles will be undefended and an enemy could easily put 90 soldier on Castle 10 and 1 soldier on each undefended castle winning the war. So Castle 1 is defended by 19 soldier to be able to defended the rest of the castles with 1 soldier. Running a simulation with a random number generator gives me a 98% chances of winning with this combination, althought it is sunday night and I might have made some fundamental mistake in the code |

16 | 16 | 18 | 18 | 2 | 18 | 18 | 18 | 2 | 2 | 2 | 2 | To disrupt strategies that rely on lower value castles. |

17 | 17 | 16 | 16 | 16 | 16 | 16 | 16 | 1 | 1 | 1 | 1 | Evenly distributing troops at 6 castles gives me a great chance to win a simple majority, and single troops at the remaining 4 gives me an auto win if my enemy leaves any empty. |

18 | 18 | 16 | 11 | 11 | 11 | 11 | 18 | 19 | 1 | 1 | 1 | I can get 28 points out of 55 from the lower 7 castles so concentrate force there. Send a token soldier to the top castles in case someone tries a more extreme version of my strategy. Bias soldiers towards castles 6 and 7 because a 'aim at the higher castles' strategy is likely to still be interested in those. Send a few more to castle one because I could see a strategy of going for the top three castles and the lowest one. |

19 | 19 | 15 | 14 | 14 | 14 | 14 | 14 | 15 | 0 | 0 | 0 | Target to win is 28 points. Concentrating deployment on highest-value castles means I need to capture 10, 9, 8 and 1 to reach target. Highest-value castles are likely to draw most troops by my opponent. So I am going to focus on capturing enough castles from the lowest value upwards until I hit the target, which is castles #1-7 inclusive. Divide troops equally, with the spares focused on 1 (crucial to the 10-9-8-1 strategy set out above) & 7 (because it is the highest value of my targeted castles). |

20 | 20 | 15 | 13 | 13 | 14 | 14 | 14 | 14 | 1 | 1 | 1 | Contrarian strategy to go for bottom 7 (which sums to 28) rather than 10+9+8+another. Putting 1 on 8,9,10 to beat people who may use a similar strategy but forget that by getting these higher ones they win vs similar strategies. Higher on 1 to beat strategies that realize that 10+9+8+1=28 and guess 100/7=14 is lowest bound to beat on 1 (and assume people would pretty much always put the least amount of soldiers on castle 1). Even if using 10+9+8+other, unlikely to use higher than 12 or 13 on the lower castle because of the need to focus on top heavy. Strategies that assign soldiers based on castle value mostly beaten (unless using smoothing factor but this would lose to most top heavy strategies). Also beats 10 everywhere. Will see! |

21 | 21 | 15 | 7 | 8 | 5 | 5 | 11 | 10 | 11 | 10 | 18 | People want 1 and 10 so I'm fortifying them |

22 | 22 | 15 | 5 | 10 | 12 | 15 | 1 | 12 | 10 | 5 | 15 | Assuming opponents will want to send large forces at the beginning and end of their siege I fortified the first and last castles with relatively more troop. Same with the middle castle. The solitary soldier in castle six is a sacraficial lamb. Knowing I am bound to lose a castle or two, I am presuming that I can give up one castle to properly fortify more and eventually win the battles. |

23 | 23 | 15 | 3 | 7 | 10 | 15 | 19 | 25 | 2 | 2 | 2 | There are 55 total points available. Half-.5 of those are up for grabs in just the top three castles. So a strategy to just hold the top 3 castles would fall barely short of success; a strategy of holding the top 3 castles plus Castle 1 would barely succeed, and Castle 1 might be viewed as the lowest-cost place to pick up that one needed point. Assuming that most people will gravitate towards this upper-tier strategy, I chose to do something that would win against it. |

24 | 24 | 15 | 1 | 1 | 1 | 2 | 2 | 3 | 25 | 25 | 25 | Need 28 pts to win a war. I assumed there are no loser points in war. I considered various strategies, even dist, weighted dist, lower focus to 28 pts, upper focus to 28 pts, and a few variants before settling on the above which seemed to have the best results. |

25 | 25 | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 17 | 26 | 42 | Submission #5. I guess I have the second most confidence in this (of my 6 submissions). Defending just enough points/castles to win and dividing them unequally in (probably vain) hopes that I can win. |

26 | 26 | 14 | 14 | 14 | 14 | 14 | 15 | 15 | 0 | 0 | 0 | To win a war I need 28 victory points (round up half of the total number of available points). Figure most people are going to try to target the high value targets (8,9,10) which together make 27 points. So if I can capture the rest, I win. |

27 | 27 | 14 | 14 | 14 | 14 | 14 | 15 | 15 | 0 | 0 | 0 | With limited math skills, my basic thinking is that in this 1v1 scenario I just need 28 points to be victorious since the total number of points is 55. 1+2, +7 = 28, where 8+9+10 = 27. So I'm able to capture the first 7 castles while leaving my opponent to deploy most of his troops on the higher value castles (because who wouldn't normally want the highest value castle?) then I have the highest chance of succeeding and capturing 28 points. Hope I won. PS I see that double half-zip. |

28 | 28 | 14 | 14 | 14 | 14 | 14 | 15 | 15 | 0 | 0 | 0 | You need 28 points (a majority of 55) to win. I am guessing that it will be easier to do that if I focus all of my troops on 1-7 and none on 8 through 10, because I think the majority of people will overvalue those. |

29 | 29 | 14 | 14 | 14 | 14 | 14 | 14 | 16 | 0 | 0 | 0 | There are 55 points total, and I need 28 to win. Most people will concentrate on the higher numbers. |

30 | 30 | 14 | 5 | 6 | 8 | 10 | 12 | 14 | 10 | 10 | 11 | Long story short, a ton of meta-gaming. I'm an avid gamer, so analyzing strategies that are in 'meta' is something I do often. I developed 6 (really 3 archetypes) solid strategies, which would each win in a random environment. The 'uber meta' strategy that won against every strong, solid strategy whilst still being able to win an 'average' game against randoms was this one, developed out of my "Empty Castle" strategy. I know this may sound pretentious, but if I win, I would very much like to show you my "strategy notes". They're too complicated to describe in words, but pictures could give you a better idea. Cheers! |

31 | 31 | 13 | 13 | 13 | 14 | 14 | 15 | 15 | 1 | 1 | 1 | Need 28 points to win = win castles 1 through 7. Spread troops close to evenly among those castles and put 1 troop each on 8-10 in case opponent is using similar strategy. |

32 | 32 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 3 | 3 | 3 | I chose this troop deployment because 28 victory points are needed to win. Therefore, if I won all of the lowest 7 castles, then I'd win, but I put some on the last three in case someone else highly concentrates their troops in other places. |

33 | 33 | 13 | 7 | 17 | 8 | 11 | 6 | 13 | 7 | 9 | 9 | Had some wars on excel tempted to do a straight 10 per castle though. |

34 | 34 | 13 | 7 | 10 | 13 | 16 | 19 | 22 | 0 | 0 | 0 | forfeit on 8,9,10, overweight 1, |

35 | 35 | 13 | 3 | 13 | 31 | 24 | 11 | 1 | 1 | 2 | 1 | I figured people would go after the later castles and keep their deployments balanced |

36 | 36 | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 29 | 29 | 29 | Seeing as there are only 55 total points available, you only need 28 victory points to win. The "easiest" way to do this (in terms of total number of castles won) is Castles 1, 8, 9 and 10. I then split the number of soldiers such that the ratio of soldiers at castles 8 to 9 to 10 is 1:1:1 and the number of soldiers at castle 1 is greater than 10. This strategy will beat anyone who splits evenly between the 10 castles, and (I'm hoping) will beat a decent number of people who go for the same four castles. An example strategy this would lose to is is someone split all 100 of their troops between e.g. Castles 9 & 10. I decided not to employ a similar strategy since I think more people will try something similar to mine rather than something somewhat counter-intuitive like betting all their troops on only two castles (although this isn't really based on any evidence). |

37 | 37 | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 29 | 29 | 29 | Focus all troops on the fewest number of castles that would win the minimum 28 points necessary to win. |

38 | 38 | 12 | 12 | 12 | 12 | 15 | 17 | 20 | 0 | 0 | 0 | I gave up 3 castles and tried to win 7. My hope was that others would try to win the high point bases and I would therefore be able to steal the bottom bases and the win. |

39 | 39 | 12 | 12 | 12 | 12 | 13 | 13 | 26 | 0 | 0 | 0 | I assumed that the most popular strategies would be a distribution close to 10 everywhere, a distribution close to putting a number of solders in each castle equal to (100 * castle # /55) and strategies which only attack castles 7 through 10. This strategy requires that I win castles 1 through 7 so each castle is worth the same to me, except I need to make sure I steal castle 7 from the people only going for 7-10 (and one of the variations there is to play 25 soldiers across the board). |

40 | 40 | 12 | 12 | 12 | 12 | 13 | 13 | 13 | 13 | 0 | 0 | Trying to make them waste troops on 9-10 |

41 | 41 | 12 | 12 | 12 | 12 | 12 | 12 | 26 | 1 | 1 | 0 | Beat the 10x10 strategy or any that over values the last 3 castles. If you win 7 you have 28/55 pts. |

42 | 42 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 2 | 2 | I does not matter if I lose more than one castle from 1-8. None are more important than the other. 7/8 in any combnation wins here. I choose to use 2 in castle 9 and 10 to pick off empty castles or somebody that chooses to put 1 in there. |

43 | 43 | 12 | 12 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | Just enough to trip up a full 10-10 average deployment (maybe? :) ) |

44 | 44 | 12 | 12 | 2 | 4 | 4 | 11 | 19 | 10 | 18 | 8 | Used a random number formula which summed to 100. Recalculated a few times to get some heavier numbers near the castles 6-9, since I assumed most people would heavily load castle 10. |

45 | 45 | 11 | 12 | 13 | 14 | 15 | 17 | 18 | 0 | 0 | 0 | While last few castle have most points, they are also more heavily defended. I am shifting my troops down the order, and give up the big castles. Smaller castles are easily overwhelmed by the extra troops I placed. |

46 | 46 | 11 | 12 | 13 | 14 | 15 | 17 | 18 | 0 | 0 | 0 | There are 55 total points available, so 28 points are necessary to win. I figure a lot of people will focus on winning the high value castles, so I will focus on winning enough low value castles. I didn't think about this strategy very long, but I hope I beat somebody. |

47 | 47 | 11 | 12 | 13 | 14 | 15 | 16 | 19 | 0 | 0 | 0 | Out of 55 points you want 28. You want to put more troops in higher valued castles, however by using only 1-7 (and conceding the highest 3 castles) I can reach the necessary 28 points. I divided it evenly between the castles with a singly increasing importance on each higher castle. The added remainder went to the highest sought after castle. |

48 | 48 | 11 | 12 | 13 | 14 | 15 | 16 | 19 | 0 | 0 | 0 | sum of points for winning castles 1-7 is greater than points for 8-10. i'll let others win those. need to be able to beat people that send 1/10 to every castle, so castle #1 needs at least 11 soldiers. increased by one up to castle #6, then send the rest (19 soldiers) to castle #7 |

49 | 49 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 0 | 0 | 2 | We only need to get 28 of the 55 victory points to win. Castles 1-7 deliver that for us. Let others focus on trying to get Castles 8-10. Put a leftover 2 on 10 to counter anybody else trying a similar strategy of ignoring Castle 10. |

50 | 50 | 11 | 11 | 12 | 14 | 14 | 18 | 20 | 0 | 0 | 0 | The goal is not to win all the castles; the goal is to win the majority of the 55 points possible. I assume that more people will focus on winning the higher point values (7, 8, 9, 10) so I will take the opposite strategy. I can win 28 points if I win castles 1-7, so I split my troops among those castles, more or less equally. I can assume that, if people try a 1/8/9/10 strategy, they will not weight 1 as highly. |

51 | 51 | 11 | 11 | 12 | 13 | 14 | 16 | 20 | 1 | 1 | 1 | Beats strategies that choose 10 equally, prioritizes the first 7 castles since 1+2+3+...+7=28 > 55-28 = 27. 1 bids on Castles 8-10 to deter people from not putting any troops in those areas at all. |

52 | 52 | 11 | 11 | 11 | 13 | 16 | 18 | 20 | 0 | 0 | 0 | I chose to not contest 8, 9, and 10 which may be attractive to go after since they are the highest point value castles, and save my troops for going after castles 1-7. If you are able to win castles 1-7, you automatically will win with a score of 28-27. I chose to at least put greater than 10 soldiers at each castle that I wanted to contend for, such that I would win if my opponent distributes evenly (i.e. 10 soldiers at each castle), that I would still win castles 1-7. I then increased my troop levels for castles 4-7 such that all 100 soldiers were distributed, with castle 7 receiving my most troops, in case my opponent tries to stack all or most of their soldiers at the higher value castles. Additionally, if my opponent also puts 0 troops at castles 8-10, we would split points and I would have a chance for an even larger number of victory points. |

53 | 53 | 11 | 11 | 11 | 12 | 12 | 13 | 27 | 1 | 1 | 1 | Half of available points is 27.5. If I win castles 1-7, that is 28. If someone distributed evenly I want more than 10 on the lower castles. If they try for the top 4 I want to have more than 25 on castle 7. If they try for a relative expected value strategy I want more than 12 on castle 6. If they try my strategy (bottom 7) I want to steal castles 8-10 with the minimum number of troops. |

54 | 54 | 11 | 11 | 11 | 11 | 13 | 17 | 26 | 0 | 0 | 0 | Castles 1-7 are enough to get the majority of the points. This allotment defends against putting 10 in every castle and putting 25 in the top 4 castles, and should beat many strategies that focus on seriously competing for the top castles. |

55 | 55 | 11 | 11 | 11 | 11 | 12 | 16 | 22 | 2 | 2 | 2 | I did not put a focus on the top 3 numbers because if I captured the bottom 7 I would win, and I figured others would place a large amount in the 10-9-8 castles. I would have no real ability to guess the arrangement others used for the big 3, so I went small. I believed I needed to be able to beat a 10 soldier in every castle lineup, so I needed at least 11 soldiers in every castle numbered 1-7. I decided the 7 castle was likely my most important, so I wanted to creep the people creeping 20. With the 6 I creeped 15, and the 5 I creeped people creeping 10. All of the other low castles I creeped 10. In order to beat others running a low castle strategy I creeped people putting 1 in the 10-9-8 castles. |

56 | 56 | 11 | 11 | 11 | 11 | 12 | 12 | 26 | 2 | 2 | 2 | To win each round, you only need to win 28 points. Winning any more than 28 points doesn't do you any good - a win is a win, whether by 1 point or 10 points. I identified what I believe will be popular strategies, and developed one that can beat them. I suspect the most popular strategies will be the Even All Strategy, the Top 4 Strategy, and the Bottom 7 Strategy. I also believe some players will employ versions of the Marginal Strategy, which I employ here. I am playing what I call the Marginal-Low Strategy. This troop deployment is susceptible to a variation of the Even Strategy that evenly distributes forces to a smaller number of castles, rather than 10 across the board. |

57 | 57 | 11 | 11 | 11 | 11 | 12 | 12 | 26 | 0 | 0 | 6 | I basically tried to come up with a solution that would beat the most common solutions I could think of. Being that I had no idea what others would submit, seemed like the best thing to do. |

58 | 58 | 11 | 11 | 11 | 11 | 11 | 22 | 23 | 0 | 0 | 0 | Over half the points are in 1 - 7 (28) vs (27) in 8, 9, 10. This will beat an even spread of 10 x 10, or 5 x 20 in the top 5 castles. This should beat most strategies that put most points into the top 3 castles. The only strategy it would lose to would be a 6 -10 castle strategy that weighted its troops to castles 6 and 7, not 9 and 10 - which seems an unlikely strategy to take and would lose to the commonsense strategy of putting more troops in 8, 9 and 10. |

59 | 59 | 11 | 11 | 11 | 11 | 11 | 21 | 21 | 1 | 1 | 1 | I tested it out against all of the strats I thought people might use, and this one won against all of them |

60 | 60 | 11 | 11 | 11 | 11 | 11 | 21 | 21 | 1 | 1 | 1 | We started by examining several strategies that we expect our opponents will be likely to employ - including: (1)equal distribution strategy across all castles, (2) gradient strategy with highest deployment at castle 10, (3) sacrificing castle 10, with gradient starting at castle 9, (4)sacrificing 10 and 9, with gradient starting at castle 8, (5)sacrificing 10, 9 and 8 with gradient starting at castle 7, (6)equal distribution across all even numbered castles, (7)equal distribution across all castles from 1-7. We then distributed our soldiers in a fashion that would defeat all of these seemingly reasonable strategies. Bring it on arch-enemies! |

61 | 61 | 11 | 11 | 11 | 11 | 11 | 21 | 21 | 1 | 1 | 1 | cuz why not, lol |

62 | 62 | 11 | 11 | 11 | 11 | 11 | 20 | 25 | 0 | 0 | 0 | I'm attempting to maximize my odds of getting 28 points out of a possible 55, this guaranteeing victory. I'm ceding 8-9-10 thinking most people will throw all their troops that way. I'm also thinking there will be enough people who assign 10 troops per castle, which is why I put 11 troops on the lower numbers. |

63 | 63 | 11 | 11 | 11 | 11 | 11 | 19 | 26 | 0 | 0 | 0 | I enjoyed this weekäó»s Riddler. I attacked it, not mathematically, but by brute force and trial näó» error. I learned that the best strategy would involve trying to win a few key battles (i.e. not all of them), loading to ensure victories in those battles, and that it would entail barely winning in the end; i.e. a small margin of victory. My first thought was to look at ways to lock up the highest-value castles. Winning the battles for the top 3 castles is 27 points, only 1 short of victory, so my approach involved throwing a lot of soldiers at the top 3, a chunk at a lower-value one, and deploying 1 soldier at the remaining ones (to win battles against zero soldiers). An example of this approach is 0-2-1-1-1-1-1-30-31-32. This wins against many strategies but fails against a simple one of 10-10-10-10-10-10-10-10-10-10. Loading up on one lower-value castle to 11 (to defeat that strategy) leads to too few soldiers at the higher-value castles. Then I thought of the opposite approach; i.e. concede the battles for the 3 higher-value castles and try to win the remaining 7 (which would yield 28 points, and a win). The best approach I found was 11-11-11-11-11-19-26-0-0-0-. The 26 is necessary to defeat a strategy of deploying Œ_ of oneäó»s soldiers (i.e. 25) to each to the top 4 castles, the 11 is to beat the 10x10 strategy, and assigning the remaining 8 soldiers to the 5th highest castle. This strategy works against almost every strategies, especially the ones that many people likely would choose. It fails against strategies involving loading up on the mid-value castles; e.g. 0-0-1-4-11-20-25-20-15-4. However, as those strategies lose to many other ones I thought people would not choose them. |

64 | 64 | 11 | 11 | 11 | 11 | 11 | 19 | 21 | 1 | 2 | 2 | Made up some simple strategies (10 each, top 3 heavy, bottom 7 only, proportional to points) and this beat all my toy scenarios. Then among those playing for the bottom 7 I wanted to sometimes steal one of the big castles if they leave them wide open, and also weight toward the 6th and 7th castle to hopefully win those against similarly minded players and also win from some people doing something proportional to points but giving up on a few bottom categories or going after 5 columns 20 each. |

65 | 65 | 11 | 11 | 11 | 11 | 11 | 16 | 25 | 1 | 1 | 2 | The name of the game is getting to 28 Victory Points. If you win Castles 1-7, you reach 28, and the remaining castles are useless. Therefore, it makes sense to load heavily on 1-7 while virtually ignoring 8-10. I chose to throw a point or two on the big ones, just in case someone else uses the same strategy, but chooses zero for any of the top three. Also, using this strategy requires more than 10 on every value 1-7, because otherwise it would fail against an even distribution of 10 per castle on tie breakers. |

66 | 66 | 11 | 11 | 11 | 11 | 11 | 14 | 25 | 2 | 2 | 2 | Winning 1-7 or 7-10 wins enough points to win the war. This makes 7 the most important castle. I chose the low points strategy, assuming it would be the least used, and that people that go high, will dump more points on 10. So the plurality of my points go to castle 7 to win it. I put 2 points on 8-10 to win any zeros and ones (for the people throwing a token army at the high numbers). |

67 | 67 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 12 | 0 | I figure everybody will divert too many for castle 10, so I divided up for the remaining |

68 | 68 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 1 | Hopefully people divide equally, and this maximizes my chances against such players. If they do, I win 9 of 10, and lose castle 10 |

69 | 69 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 1 | Assume everyone else will over-allocate to castle 10. Sacrifice and make up points elsewhere. |

70 | 70 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 1 | |

71 | 71 | 11 | 2 | 11 | 11 | 11 | 2 | 12 | 36 | 2 | 2 | I assumed a whole bunch of people smarter than me were spending hours on the mathematically best way to deploy your troops, so I went with an opposite approach: Randomly guess which castles to deploy to, while aiming to gain 28/55 possible victory points. I chose castles 1,3,4,5,7,8 and weighted more heavily towards to castles worth more points. I chose 11 as a minimum so that I couldn't easily lose to someone who just put 10 troops in each castle, and 36 in castle 8 so that someone with the 1-8-9-10 strategy also wouldn't win. I also killed about 10 minutes at work, so I'm pretty happy. |

72 | 72 | 11 | 1 | 12 | 1 | 15 | 1 | 19 | 19 | 20 | 1 | Trying to maximize expected value knowing my opponent will be doing the same thing. |

73 | 73 | 11 | 1 | 1 | 1 | 1 | 1 | 1 | 26 | 26 | 31 | Go For 28 points |

74 | 74 | 11 | 1 | 1 | 1 | 1 | 1 | 1 | 25 | 27 | 31 | There's 55 points, so you need 28 to win. 10+9+8+1 = 28; that's the fewest number of wins. Guard against people splitting their troops 10 ways by sending 11 to Castle 1, and don't leave anything uncontested by not sending any. That's 11 + 6 = 17, with 83 to spread out between Castles 8 - 10. I didn't overthink this. |

75 | 75 | 11 | 1 | 1 | 1 | 1 | 1 | 1 | 20 | 29 | 34 | There are 55 total points available, so you need 28 points to win, which is why I focused on castles 1, 8, 9, and 10. Winning those four castles gets me exactly 28 points. Assuming an average of 10 soldiers per castle, placing the amount of troops I put in each of these four castles should hopefully let me prevail more often than not and get the 28 necessary points to win the Battle Royale and rule Riddler Nation. |

76 | 76 | 11 | 0 | 1 | 1 | 1 | 1 | 1 | 25 | 28 | 31 | Assume enemy will try to be clever and will have assumed that I am targetting large castles. He will have allocated his troops to win lower castles. So I try to win the point total by reallocating to win castles 8, 9, 10, and 1. In case any of the middle castles (3-7) are ignored, send 1 soldier to prevent a point split and steal the win. |

77 | 77 | 11 | 0 | 0 | 2 | 3 | 3 | 3 | 26 | 26 | 26 | The easiest way to win is to win {1, 8, 9, 10} for 28 v 27. The strategy needs to counter: [*] Strategy who tries to win {7,8,9,10} and goes all-25: This means that {8,9,10} must have at least 26 soldiers. [*] Strategy who splits 10 soldier to all: This means that {1} must have at least 26 soldiers. This means we have 1 : 11 8 : 26 9 : 26 10 : 26 remaining 11 soldiers The only enemy for this strategy would be strategy who goes kamikaze and play for {9,10} and goes split-50. The remaining 11 soldiers is split for {4,5,6,7} to make up for the 19 points loss from the kamikaze play. |

78 | 78 | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 29 | 29 | 31 | |

79 | 79 | 10 | 11 | 12 | 13 | 15 | 17 | 22 | 0 | 0 | 0 | I think people may gravitate toward locking down high numbers. |

80 | 80 | 10 | 10 | 20 | 30 | 5 | 5 | 5 | 5 | 5 | 5 | I can capture the lower numbers while everyone else is fighting over the higher numbers. |

81 | 81 | 10 | 10 | 11 | 12 | 12 | 13 | 26 | 2 | 2 | 2 | go for the lower castles to get 28 points |

82 | 82 | 10 | 10 | 10 | 15 | 15 | 20 | 20 | 0 | 0 | 0 | I figure castles 1-3 will be lightly deployed while 4-7 will be slightly more defended. But I expect most will focus on the big targets. If I can win castles 1-7 and "sacrifice" 8-10, they will only have 27 points. I will have 28 points and still win the war. |

83 | 83 | 10 | 10 | 10 | 11 | 11 | 12 | 12 | 12 | 12 | 0 | In most scenarios, it would beat what I'd plan if I was being lazy. |

84 | 84 | 10 | 10 | 10 | 10 | 15 | 20 | 25 | 0 | 0 | 0 | I know I need 28 pts to win. Taking castles 1-7 gives me 28 pts. Many people will likely put a large # of troops on one or more of the bigger point value castles. Of course, many people will think of this and do the opposite, making my theory kaput. |

85 | 85 | 10 | 10 | 10 | 10 | 15 | 20 | 25 | 0 | 0 | 0 | If you win castles 1-7 you win the game. This strategy hopes the enemy will waste all or most of its army's to win 8-10, and not be prepared to win any one of the remaining castles. |

86 | 86 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | If my opponent also places ten at each castle, we tie. At worst, I win half the match-ups, and we tie again. But if my opponent places more than ten at one or more castles, chances are I'll win more points. |

87 | 87 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | Uniform Distribution |

88 | 88 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | |

89 | 89 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | Maximin |

90 | 90 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | Guaranteed to win at most half the points per battle (55) to at least Castles 1-5 (15) |

91 | 91 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | Just a wild guess at a strategy that might stand up against the widest array of possible configurations. |

92 | 92 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | Not sure |

93 | 93 | 10 | 10 | 7 | 5 | 7 | 7 | 16 | 11 | 13 | 14 | set.seed(154) poo <- sample(1:10, 100, replace = T) table(poo) |

94 | 94 | 10 | 8 | 8 | 13 | 8 | 20 | 30 | 1 | 1 | 1 | There are a maximum of 55 Points available, so 28 is a Winning score. My strategy is to win the first 7 castles to get 28 points, hoping my opponents over commit solders to the last 3 castles. I have also overcommitted to castle 1 as Castle 1,8,9,10 is a winning strategy same applies to castle 4 as 4,7,8,9 is a winning combination. |

95 | 95 | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 27 | 28 | 29 | The plan is to get to the 28 points needed with as few castles as possible while also leaving a guard against other strategies that assign zero soldiers to some castles. |

96 | 96 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 30 | 30 | If I win castles 1,8,9,10 I will receive 28 points and my opponent will only receive 27. This is the least number of castles that I need to win in order to beat my opponent. Assuming that I need to win all 4 to have a chance and that my opponent will put very little into winning a single point from castle 1, I will only deploy 10 soldiers. Winning castle 1 is a lynchpin though and I need to win it or my theory fails. All other castles are very important to me and I am able to put 30 soldiers in castles 8, 9, and 10 because castles 2-7 mean nothing to me. I can lose them all and still win if I win 1,8,9,10. |

97 | 97 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 30 | 30 | Load up the soldiers on the minimum castles needed to win |

98 | 98 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 30 | 30 | Tried to choose the fewest number of castles (and in the case of #1' the least likely to be attacked) to attack that would give me a majority of the points. |

99 | 99 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 30 | 30 | Deploying hopefully overwhelming force at castles 8 through 10, and a token force to capture 1. It doesn't allow any room for failure, but hopefully will be strong enough at the one point to ensure victory. |

100 | 100 | 9 | 12 | 13 | 14 | 15 | 16 | 17 | 1 | 1 | 2 | I attempt to concede castles 8-10 to win 1-7 in order to scrape by with a total win. I moved one extra soldier from 1 to 10 in case someone puts 1 in the last 3 castles, but otherwise uses the same strategy. |

### Advanced export

JSON shape: default, array, newline-delimited

CREATE TABLE "riddler-castles/castle-solutions" ( "Castle 1" INTEGER, "Castle 2" INTEGER, "Castle 3" INTEGER, "Castle 4" INTEGER, "Castle 5" INTEGER, "Castle 6" INTEGER, "Castle 7" INTEGER, "Castle 8" INTEGER, "Castle 9" INTEGER, "Castle 10" INTEGER, "Why did you choose your troop deployment?" TEXT );