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

Ages

Ages (1)^**/*****
“Did you know that this year the sum of our ages is a multiple of 8?” Jill asked John.
“Yes,” Tom answered. “And did you know that next year the product of our ages is a three digit number consisting of three times the same digit?”

Ages (2)^**/*****
“What a coincidence,” Bill said, who had overheard their talk. “Next year the product of the ages of Bess and me will also be a three digit number consisting of three identical digits. But this year the sum of our ages is a two digit number consisting two identical digits.”

What are the ages of John, Jill, Bill and Bess?

You can check your solution here

Bongard problem 19

Which rule satisfies the 6 figures on the left but is obeyed by none of the 6 figures on the right?
1)Bongard problem 19^**/*****

In 1967 the Russian scientist M.M. Bongard published a book containing 100 problems. Each problem consists of 12 small boxes: six boxes on the left and six on the right. Each of the six boxes on the left conform to a certain rule. Each and every box on the right contradicts this rule. Your task, of course, is to figure out the rule.

You can check your solution here

You can find more Bongard problems here on this site and at Harry Foundalis’ site.

New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.