Polar bears and other dice puzzles

Polar bears is no doubt the most famous dice puzzle around. I first heard it when I studied mathematics, and Douglas Hofstadters book “Godel, Escher, Bach” may have been the source.
If you want to puzzle your friends, roll 5 dice, and tell the how many polar bears can be spotted. Then roll 5 dice again, let them guess, and tell them the correct number if they guess wrong.

1) Polar bears***/*****
The polar bears puzzle is traditionally presented as a throw of 5 dice. If you are stumped, don’t despair, it is rumored that Bill Gates could only partially solve it.

Even though you may find it hard, I do encourage you to try to solve it before consulting the answer.

You can check your solution here

2) Seals***/*****
Polar bears hunt for seals. How many seals do you count?
This puzzle is inspired by the authors of https://www.pleacher.com/handley/puzzles/polrbear.html.

You can check your solution here

3) Fish***/*****
This puzzle too is inspired by the authors above, though in both instances I changed names to get a more logical picture.

You can check your solution here

1 thought on “Polar bears and other dice puzzles

  1. This puzzle hit a group of teachers at Rutgers University in 1991 and At that time it was discovered that the polar bears hunt for fish and the fish eat plankton. How many plankton are there? Yes there is a legitimate algorithm for determining the number of plankton for any given dice roll.

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