Brain Teasers and Puzzles

Brain teasers, puzzles, riddles, and other challenges

Polydivisible Number

A polydivisible number is a number for which the first n digits form a number evenly divisible by n for all n between 1 and the number of digits of that number.

In other words, the first 2 digits form a number divisible by 2, first 3 digits form a number divisible by 3, first 4 digits form a number divisible by 4, etc. for all of the digits of the number.

Can you arrange the digits 1-9 to form a 9-digit polydivisible number? Each digit 1-9 must be used exactly once.

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Confusing Zip Codes

The U.S. uses 5-digit zip codes to help determine where mail goes. Since mail can be oriented in all sorts of directions, they avoid assigning zip codes that could be confused with a different zip code when read upside-down. For example, 61666 could be confused with 99919 when upside-down, so mail could be accidentally routed to the wrong zip code if both were actual zip codes.

How many zip codes could be confused with a different zip code when read upside-down?

In the example above, 61666 and 99919 would count as two confusing zip codes. Also, zip codes are allowed to start with 0, such as 00501.

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Last Chocolate Game

Two friends are playing a game with two boxes of chocolates. They take turns taking out some number of chocolates from the boxes, and whoever takes the last chocolate wins. Each turn they can take chocolates one of two ways:

  • Take any number of chocolates from a single box
  • Or take an equal number of chocolates from each box

If there are 25 chocolates in one box and 35 in the other, what is the winning strategy?

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Vacant Room Probability

Your workplace has a phone room for employees to quietly make personal calls. The room has no windows, just a sign that can be switched from “Vacant” to “Occupied”. However, employees differ in how consistently they use the sign:

  • 1/2 of them always switch to “Occupied” when they enter and “Vacant” when they exit.
  • 1/4 of them ignore the sign altogether – the sign will always read the same before, during, and after their visit.
  • 1/4 of them always switching to “Occupied” when they enter, but always forget to switch back to “Vacant” when they exit.

If the room is actually occupied exactly 1/2 of the time, what is the probability the room is actually vacant when the sign reads “Vacant”?

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