Brain Teasers and Puzzles

Brain teasers, puzzles, riddles, and other challenges

Sicherman Dice

Sicherman dice are a particular pair of six-sided dice that, when rolled, produce sums with the same probability distribution as a pair of standard six-sided dice. In other words, these dice do not have the arrangement of 1, 2, 3, 4, 5, and 6 on their six sides, but when rolled together, still produce the same distribution of sums:

  • One way to roll a 2
  • Two ways to roll a 3
  • Three ways to roll a 4
  • Four ways to roll a 5
  • Five ways to roll a 6
  • Six ways to roll a 7
  • Five ways to roll a 8
  • Four ways to roll a 9
  • Three ways to roll a 10
  • Two ways to roll a 11
  • One way to roll a 12

Sicherman dice are the only alternative arrangement of six-sided dice with positive integers that produce the same probability distribution as a pair of standard six-sided dice. Can you figure out what numbers belong on Sicherman dice?

Hint: One of the dice has no numbers greater than 4.

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Who Scored How Many Points

Lalo, Tyson, and Michael played a number of games of pick-up basketball. At the end, their combined points across all the games were:

  • Lalo: 20
  • Tyson: 10
  • Michael: 9

They noticed that in every game, one of them scored x points, one of them scored y points, and one of them scored z points, where x > y > z and all three are distinct positive integers.

If Tyson got the highest score in the first game, who got the second highest score in the second game?

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Double the Amount You Need to Do

At the beginning of January, you set a goal to work every day, to reach a total of 5000 minutes of work by the end of the month. But to give yourself a better shot of achieving this, you decide to front-load it—at the beginning of each day, you figure out how much you’d need to work on average on each remaining day to achieve your goal, and then you work double the amount you need to do. For example, if you had 50 minutes left and 5 days left, you would need to work 10 minutes/day, so you would choose to work 20 minutes on that 5th-to-last day.

If you chose to work this way, how long does it take you to complete your goal of 5000 minutes?

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Stranded in the Wilderness Brain Teaser

A man is stranded in the wilderness, in a remote northern area. There’s a lake nearby, and utility poles carrying electricity, presumably to a nearby town. However, there’s no way he can make it to the town in the freezing cold weather.

The man has a dinghy, two paddles, and an axe, but no devices that can communicate with anyone and no way to make a fire.

How does the man manage to get rescued as quickly as possible?

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Coin Rotation Paradox

The coin rotation paradox is a famous math problem with an unintuitive solution:

If you roll a coin around the edge of another coin of the same size, from an external perspective, how many rotations does the coin make by the time it returns to its original position?

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Giant Cat Army Riddle from TED-Ed

In Dan Finkel’s TED-Ed video, he shares this math puzzle, paraphrased as follows:

Dr. Schrödinger is creating an army of giant cats for villainous purposes. Your team of secret agents has located his lab, but needs to get through his unusual security system.

The system displays a single number, and has three buttons that control this number:

  • Add 5
  • Add 7
  • Take the square root of the displayed number

Goal: make the numbers 2, 10, and 14 show on the display, in that order.


  • The display starts at 0.
  • It’s fine if other numbers are displayed in between 2, 10, and 14, as long as they appear in that order.
  • The system will malfunction if any number is displayed more than once.
  • The system will malfunction if any number greater than 60 is displayed.
  • The system will malfunction if any fraction/decimal is displayed.

How can you achieve this?

(Sorry, the giant cat army has nothing to do with the puzzle.)

Source: Dan Finkel and TED-Ed

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