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Riddler - Solutions to "Pick A Number, Any Number": low_numbers.csv

This directory contains the data behind the puzzle Pick A Number, Any Number. A discussion of the solution is in the following week's puzzle.

Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub

3,660 rows sorted by Show Your Work

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Link rowid Your Number Show Your Work ▼
340 5  
518 9  
841 16  
854 17  
1240 25  
1771 41  
3314 351  
3337 403  
3449 721  
3116 193 Assuming 1500 entries, assuming a Zipf distribution, the number choosing 1 would be 1500/7.89 ~ 190. The Zipf distribution is: n, n/2, n/3, n/4, n/5, n/6, ... (i.e the harmonic series). The 7.89 is the sum of the harmonic series out to 1500. So the expected value of the number choosing a particular interger drops to 1 at about 190. So the lowest unused number is probably around there. If we think of this as an n person zero sum game, then it depends on whether n is even or odd. If n is odd (= 2*k + ), then any alliance of k + 1 players can force a win by choosing all the numbers from 1 to k + 1. At least 1 of them must be unique. If n is even (= 2*k), then any alliance of k players can force a tie by choosing all the numbers from 1 to k. At least 1 of them must be unique, unless the other k players also choose all the numbers from 1 to k.
3029 164 say my name
3190 229 None really
350 5 .
2425 77 Hide 68, 34, 17, 85, 5, 95, 19, 38, 76, 4, 92, 46, 23, 69, 3, 87, 29, 58, 2, 62, 31, 93, 1, 39, 78, 26, 52, 13, 91, 7, 77, 11, 99, 33, 66, 22, 44, 88, 8, 56, 28, 84, 42, 21, 63, 9, 81, 27, 54, 18, 90, 45, 15, 75, 25, 50, 100, 20, 40, 80, 16, 64, 32, 96, 6, 36, 72, 24, 48, 12, 60, 30, 10, 70, 14, 98, 49 I am pretty sure there is a way to get to 78, but I can't figure it out. I looked at the primes first, saw where I could input them in my set, then I looked at numbers with only two multiples and thought of where they would have to go. From there it was a lot of trial and error.
2756 117 A guess?
2456 81 Best guess
3120 194 Don't try to quantify my art, man!
2270 67 I asked my daughter at dinner tonight, she said it was the best year for muscle cars. That sounded better than my original choice of 2 for people who initially thought 1 but then on second thought went higher and passed 2.
836 16 People wanted an interesting sounding number or a prime number or something like 167 that feels unique. I predict they shy away from numbers with lots of divisors. Also people will be afraid a very low numbers.
2074 54 X
2758 117 aribitrary chosen
2051 53 x <-abs(rnorm(1))*500
1510 34 ¯\_(ツ)_/¯
2269 67 ¯\_(ツ)_/¯
3178 221 ¯\_(ツ)_/¯
676 13 "I'm not superstitious, but I'm a little stitious"
2876 131 "show your work" this aint a math problem, you sound like my teacher 131 is good enough
567 10 "ten is a stupid number to pick, pick a weird number that nobody else will"
3623 17322 $echo $RANDOM
2049 53 'Twas my basketball number at St. Norbert College
3626 22908 (2*3*23+2+3+23)*2*3*23
3624 19683 (3^3)^3
734 14 *shrug*
1036 20 *shrug*
1200 24 *shrug*
1963 47 *shrug*
417 7 *shrugs*
259 3 -
608 11 -
1162 23 -
1173 23 -
1248 26 -
848 17 --
802 15 .
996 19 .
1477 32 .
1686 38 .
3247 267 .
3291 317 .
444 8 ...
1766 40 ...
3140 206 ...
3245 266 ...
2981 151 ...Lucky guess?
460 8 0 - 7 might be non-unique..
10 0 0 is the lowest positive integer number. People will probably try to avoid numbers they think everyone will pick, might as well pick the lowest.
6 0 0 is the lowest possible integer that is not negative.
3255 273 0-99 will be someones favorite player's jersey number. 100-199 will be suffer from the same problem but with the person adding 100 to it to beat everyone else. So the first number will be in the 200's. 273 is not prime, not a square, not a cube, etc. The most distinct thing about it is that its the triple point of water in Kelvin and might be some 14 year old's birthday.
686 13 1 + 3 = 13
118 1 1 is a terrible pick, but everyone knows that and might avoid it.
138 1 1 is a unique number -- there is no other number like it!
81 1 1 is an integer
1212 24 1 is going to be trolled. I expect prime numbers to be heavily submitted. So a prime plus 1 doesn't seem too daft.
147 1 1 is really low
97 1 1 is the lowest positive integer. Since it needs to be the lowest unique integer, I'm assuming that everyone will consider 1 to be too obvious a choice and hence unlikely to be unique. Much like my strategy would be on The Price Is Right, I'll bet $1, Bob.
261 3 1 is the obvious answer if there were only one submission... but I assume the website has more readers than just myself. Again, assuming most people will realize similarly and pick >30 again assuming the lower numbers have already been chosen by others... But what happens when everyone thinks the same thing and skips the numbers under 10. Okay, it's not 3 but I'm not a game theory expert.
124 1 1 is the smallest positive integer
2282 68 1 less than the children who will choose 69 :-)
283 4 1 or 2 is too low. When picking a random number, I suspect most people lean towards odd numbers, so, 4 it is. Probably way too low; this one seems ripe for collusion and automated entries...
1890 44 1) I assume people are more likely to choose numbers they think are unique, so more likely to choose odd or prime numbers. I will choose an even number not divisible by 10. 2) Just guessing, I'd imagine that the first sqrt(n) numbers will all be taken. I am also guessing that maybe 1000 people will play, so probably the first 32 numbers will all be taken. I'm looking for an even number greater than 32. 3) Just to fudge a bit, I'll pick 44. (42 seems too cliche a pick. 38 might be a possibility.)
128 1 1, 2, 3, 4...
377 6 1, 2, 3, 4, and 5 seem like obvious choices based on familiarity and common usage (1 is the lowest positive integer, a couple/duo/etc. for 2, lists of 3, table for 4, 5 fingers). After that, I would think most people would skip to the "lucky" number 7, leaving 6 as a, perhaps, lonely exclusion. Beyond that, I would think 8 or 9 might be reasonable choices, with response rates spiking again at 10 (our base numbering system), 13 (for being "unlucky), and then slowly declining as one moves away from the lowest number with small spikes at "round" numbers (15, 20, 25, etc.).
1843 43 1,2,3,...,43
3443 689 1,382 readers submitted responses to the original Riddler Castle problem. As this is a simple answer to give, the response rate should be higher than 1,382, however I will assume 1,382. Assuming a non-even distribution of responses, weighted to the lower half, selecting a number which is half of the estimated responses should be a good chance of being both low and unique. To ensure that the number is unique, the number is reduced by 2.
3444 691 1,538 people (an appropriate number, given this website's name) submitted an answer to the coffee question. I'm presuming a similar amount submitting for this. Rather than simply putting 1500 or so, I figure there will be a decent amount of repeats and of numbers too high, so I'm ballparking a number a hair under half of the total number of submissions, then somewhat randomized; 691 is prime.
3410 566 1,538 people responded to who can drink the most coffee, so I assume around 1,538 people will submit answers to this riddle. I want to distribute their numbers logarithmically, with more people submitting low numbers. I chose the formula y = -ln(x/1538), with y being the number chosen and x being the number of people choosing that number. 566 is the lowest value for y with less than 1 people choosing it.
1068 21 1-10 are gonna get tried, 11-20 are probably gonna be filled with people too clever to pick 1-10, so i'm too clever for those. So 21! Hot damn! Look how Smart i as! SMRT!
753 14 1-10 are obviously out. 11and 13 are primes and will get picked. I would say 12 but I feel like someone will pick it. 14 is very boring.
631 12 1-10 has a large probability of being chosen. 11 also has a high chance.
1055 20 1-10 is too obvious, 11-19 are often people's favorite numbers, numbers ending in 5's or 0's are statistically less often chosen
1130 22 1-10 is too obvious. 11-21 is too obvious. 22 is a rare number to chose.
3059 173 1-100 are too obvious!
3512 1034 1-1000 feels like bots may get it +34 feels like a number unlikely to be picked
987 19 1-10= too easy, 11= specious choice 12= too many Tom Brady fans, 13= unlucky, 14= maybe, but still too low. 15= avoid multiples of 5 at all costs 16= too common in everyday culture, 17= plausible, but false, 18= (see #12, but for manning), 19=juuuuuuust right
1125 22 1-20 Are too common. 23 is prime and likely to be chosen. 21 is blackjack.
2048 53 1-29 was way too popular. 30-49 was a close range but in the end I wanted 50-60 and snagged a random number, 53
1500 33 1-31 all fall on days of month which could conceivably be their favorite number, 32 is going to be a popular guess because of this and so I go with next available. 33
450 8 1-5 will get selected and the likely hood of someone selecting 6,7,8 is probably close to the same
2494 86 1-50 I wasn't going to touch. When people pick random numbers they tend to pick ones with 7 - so I avoided using it. 86 felt random enough to me while still being somewhat low.
858 17 1. 7.
2509 87 1000 submissions on battle for riddler nation 2 so number should be somewhere from 1-500. Many people probably pick between 1-75 so anything greater is probably a crapshoot to be unique and be the lowest number
3499 1001 1001 is an integer
2605 102 102 is fairly uncommon, and it's low enough that most numbers won't beat it. In addition, it's not like a lot of people think of 102 as a low number.
2615 103 103 isn't a popular number. I figure everyone else will pick numbers lower than 100
598 11 11 is my favorite number!
2675 110 110 Is thought to be a uniquely unpopular number, not sure if it is a little high for this purpose...
2676 110 111-1
3520 1112 1111 + 1
3052 171 112
2802 121 11^2

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CREATE TABLE "riddler-pick-lowest/low_numbers" (
"Your Number" TEXT,
  "Show Your Work" TEXT
)
Powered by Datasette · Query took 74.009ms · Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub