Regularly.co | Puzzles for the inquisitive mind
@regularypuzzles.bsky.social
Hand-crafted puzzles made for the morning commute (https://regularly.co)
Friday's Countable number is: 969
Can you get to it only using 75, 8, 2, 10, 4, and 3?
regularly.co/countable
Can you get to it only using 75, 8, 2, 10, 4, and 3?
regularly.co/countable
December 26, 2025 at 6:00 AM
Friday's Countable number is: 969
Can you get to it only using 75, 8, 2, 10, 4, and 3?
regularly.co/countable
Can you get to it only using 75, 8, 2, 10, 4, and 3?
regularly.co/countable
How can 23 people have about a 50% chance two share a birthday? Because collisions depend on pairs, not people. 23*22/2 = 253 pairs. Each pair matches with chance 1/365. Expected matches ~253/365 ~0.69, so P(at least one) ~1 - e^-0.69 ~50%.
December 24, 2025 at 3:11 AM
How can 23 people have about a 50% chance two share a birthday? Because collisions depend on pairs, not people. 23*22/2 = 253 pairs. Each pair matches with chance 1/365. Expected matches ~253/365 ~0.69, so P(at least one) ~1 - e^-0.69 ~50%.
Wednesday's Countable number is: 707
Can you get to it only using 50, 2, 9, 8, 3, and 6?
regularly.co/countable
Can you get to it only using 50, 2, 9, 8, 3, and 6?
regularly.co/countable
December 24, 2025 at 3:10 AM
Wednesday's Countable number is: 707
Can you get to it only using 50, 2, 9, 8, 3, and 6?
regularly.co/countable
Can you get to it only using 50, 2, 9, 8, 3, and 6?
regularly.co/countable
Contrary to instinct: two losing games can add up to a winner. Parrondo's paradox. Game A loses a little. Game B uses two coins: awful when your capital is a multiple of 3, slightly good otherwise. Alternate or randomise and you spend less time in the bad state, so the combo wins.
December 23, 2025 at 8:21 PM
Contrary to instinct: two losing games can add up to a winner. Parrondo's paradox. Game A loses a little. Game B uses two coins: awful when your capital is a multiple of 3, slightly good otherwise. Alternate or randomise and you spend less time in the bad state, so the combo wins.
Tuesday's Countable number is: 668
Can you get to it only using 4, 9, 1, 7, 2, and 5?
regularly.co/countable
Can you get to it only using 4, 9, 1, 7, 2, and 5?
regularly.co/countable
December 23, 2025 at 8:20 PM
Tuesday's Countable number is: 668
Can you get to it only using 4, 9, 1, 7, 2, and 5?
regularly.co/countable
Can you get to it only using 4, 9, 1, 7, 2, and 5?
regularly.co/countable
Hiring trick: to maximise your chance of choosing the best from n unknown candidates, skip the first 37% to set a benchmark, then pick the next who beats it. This wins about 37% of the time. Why 37%? 1/e appears when you balance learning early against acting later.
December 22, 2025 at 2:00 PM
Hiring trick: to maximise your chance of choosing the best from n unknown candidates, skip the first 37% to set a benchmark, then pick the next who beats it. This wins about 37% of the time. Why 37%? 1/e appears when you balance learning early against acting later.
Monday's Countable number is: 313
Can you get to it only using 5, 1, 3, 2, 4, and 6?
regularly.co/countable
Can you get to it only using 5, 1, 3, 2, 4, and 6?
regularly.co/countable
December 22, 2025 at 6:00 AM
Monday's Countable number is: 313
Can you get to it only using 5, 1, 3, 2, 4, and 6?
regularly.co/countable
Can you get to it only using 5, 1, 3, 2, 4, and 6?
regularly.co/countable
Plot twist: Averages aren’t always above average. Simpson’s paradox: a treatment can help each subgroup yet look worse overall because the larger group pulls the mean. Change the slice and you change the story. The mean can be mean.
December 21, 2025 at 4:27 PM
Plot twist: Averages aren’t always above average. Simpson’s paradox: a treatment can help each subgroup yet look worse overall because the larger group pulls the mean. Change the slice and you change the story. The mean can be mean.
Sunday's Countable number is: 884
Can you get to it only using 50, 9, 4, 8, 1, and 10?
regularly.co/countable
Can you get to it only using 50, 9, 4, 8, 1, and 10?
regularly.co/countable
December 21, 2025 at 4:26 PM
Sunday's Countable number is: 884
Can you get to it only using 50, 9, 4, 8, 1, and 10?
regularly.co/countable
Can you get to it only using 50, 9, 4, 8, 1, and 10?
regularly.co/countable
Counterintuition: a 99% accurate test does not mean a 99% chance you are ill. If prevalence is 1% and the test has 99% sensitivity and 99% specificity, then in 10,000 people you get 99 true positives and 99 false positives. A positive is only about 50%.
December 20, 2025 at 10:05 AM
Counterintuition: a 99% accurate test does not mean a 99% chance you are ill. If prevalence is 1% and the test has 99% sensitivity and 99% specificity, then in 10,000 people you get 99 true positives and 99 false positives. A positive is only about 50%.
Saturday's Countable number is: 549
Can you get to it only using 75, 50, 25, 1, 5, and 2?
regularly.co/countable
Can you get to it only using 75, 50, 25, 1, 5, and 2?
regularly.co/countable
December 20, 2025 at 9:04 AM
Saturday's Countable number is: 549
Can you get to it only using 75, 50, 25, 1, 5, and 2?
regularly.co/countable
Can you get to it only using 75, 50, 25, 1, 5, and 2?
regularly.co/countable
Most people believe switching in Monty Hall shouldn’t matter, but here’s the thing: once the host shows a goat, switching jumps you from 1/3 to 2/3. If it still feels 50-50, which assumption about the host’s behaviour are you sneaking in?
December 19, 2025 at 2:00 PM
Most people believe switching in Monty Hall shouldn’t matter, but here’s the thing: once the host shows a goat, switching jumps you from 1/3 to 2/3. If it still feels 50-50, which assumption about the host’s behaviour are you sneaking in?
Friday's Countable number is: 543
Can you get to it only using 50, 25, 3, 9, 6, and 8?
regularly.co/countable
Can you get to it only using 50, 25, 3, 9, 6, and 8?
regularly.co/countable
December 19, 2025 at 6:00 AM
Friday's Countable number is: 543
Can you get to it only using 50, 25, 3, 9, 6, and 8?
regularly.co/countable
Can you get to it only using 50, 25, 3, 9, 6, and 8?
regularly.co/countable
Strange but true: adding a new road can slow everyone down. Braess's paradox. When drivers re-route selfishly, the equilibrium gets worse. Sometimes closing a street speeds the whole city up.
December 18, 2025 at 12:44 PM
Strange but true: adding a new road can slow everyone down. Braess's paradox. When drivers re-route selfishly, the equilibrium gets worse. Sometimes closing a street speeds the whole city up.
Thursday's Countable number is: 902
Can you get to it only using 100, 50, 75, 2, 4, and 1?
regularly.co/countable
Can you get to it only using 100, 50, 75, 2, 4, and 1?
regularly.co/countable
December 18, 2025 at 12:43 PM
Thursday's Countable number is: 902
Can you get to it only using 100, 50, 75, 2, 4, and 1?
regularly.co/countable
Can you get to it only using 100, 50, 75, 2, 4, and 1?
regularly.co/countable
Favourite pub trick: nontransitive dice. A beats B, B beats C, C beats D, D beats A. Let them pick any die first; you calmly take the one that beats it and win about two thirds of the rolls. Looks like cheating. It’s just probabilities refusing to be tidy.
December 17, 2025 at 6:56 AM
Favourite pub trick: nontransitive dice. A beats B, B beats C, C beats D, D beats A. Let them pick any die first; you calmly take the one that beats it and win about two thirds of the rolls. Looks like cheating. It’s just probabilities refusing to be tidy.
Wednesday's Countable number is: 751
Can you get to it only using 75, 100, 2, 6, 9, and 3?
regularly.co/countable
Can you get to it only using 75, 100, 2, 6, 9, and 3?
regularly.co/countable
December 17, 2025 at 6:53 AM
Wednesday's Countable number is: 751
Can you get to it only using 75, 100, 2, 6, 9, and 3?
regularly.co/countable
Can you get to it only using 75, 100, 2, 6, 9, and 3?
regularly.co/countable
The 8x8 chessboard with two opposite corners removed cannot be tiled by dominoes. Each domino covers one white and one black square; remove two of the same colour and you break the parity. Took me longer than it should to appreciate how clean that is.
December 16, 2025 at 5:57 PM
The 8x8 chessboard with two opposite corners removed cannot be tiled by dominoes. Each domino covers one white and one black square; remove two of the same colour and you break the parity. Took me longer than it should to appreciate how clean that is.
Tuesday's Countable number is: 608
Can you get to it only using 5, 10, 3, 2, 9, and 1?
regularly.co/countable
Can you get to it only using 5, 10, 3, 2, 9, and 1?
regularly.co/countable
December 16, 2025 at 5:55 PM
Tuesday's Countable number is: 608
Can you get to it only using 5, 10, 3, 2, 9, and 1?
regularly.co/countable
Can you get to it only using 5, 10, 3, 2, 9, and 1?
regularly.co/countable
Quick oddity: in a cloakroom with n people, hats are returned uniformly at random. As n gets huge, the count of correct matches stops growing and follows Poisson with mean 1. So about 37% of the time nobody is lucky, and on average exactly one person is.
December 15, 2025 at 2:01 PM
Quick oddity: in a cloakroom with n people, hats are returned uniformly at random. As n gets huge, the count of correct matches stops growing and follows Poisson with mean 1. So about 37% of the time nobody is lucky, and on average exactly one person is.
Monday's Countable number is: 887
Can you get to it only using 50, 75, 100, 25, 8, and 4?
regularly.co/countable
Can you get to it only using 50, 75, 100, 25, 8, and 4?
regularly.co/countable
December 15, 2025 at 6:00 AM
Monday's Countable number is: 887
Can you get to it only using 50, 75, 100, 25, 8, and 4?
regularly.co/countable
Can you get to it only using 50, 75, 100, 25, 8, and 4?
regularly.co/countable
Why do your friends have more friends than you on average, and do you notice that in your feed?
December 14, 2025 at 9:57 AM
Why do your friends have more friends than you on average, and do you notice that in your feed?
Sunday's Countable number is: 365
Can you get to it only using 100, 75, 50, 25, 8, and 6?
regularly.co/countable
Can you get to it only using 100, 75, 50, 25, 8, and 6?
regularly.co/countable
December 14, 2025 at 9:46 AM
Sunday's Countable number is: 365
Can you get to it only using 100, 75, 50, 25, 8, and 6?
regularly.co/countable
Can you get to it only using 100, 75, 50, 25, 8, and 6?
regularly.co/countable
Saturday's Countable number is: 485
Can you get to it only using 100, 25, 50, 7, 4, and 2?
regularly.co/countable
Can you get to it only using 100, 25, 50, 7, 4, and 2?
regularly.co/countable
December 13, 2025 at 3:20 PM
Saturday's Countable number is: 485
Can you get to it only using 100, 25, 50, 7, 4, and 2?
regularly.co/countable
Can you get to it only using 100, 25, 50, 7, 4, and 2?
regularly.co/countable
Two identical envelopes. One holds twice the other. You pick one. I offer to swap. A slick expected value calc says swapping is always better, which would make both envelopes winning. The trick is a bad prior over amounts. Where would you patch it?
December 13, 2025 at 9:30 AM
Two identical envelopes. One holds twice the other. You pick one. I offer to swap. A slick expected value calc says swapping is always better, which would make both envelopes winning. The trick is a bad prior over amounts. Where would you patch it?