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

Domino – lay out that set

Dutch puzzle designer Leon Balmaekers contacted me recently and told me he had written some booklets with puzzles for highly gifted children. The booklets are in Dutch, and contain a variety of puzzles. The highly gifted children in a classroom can make some of these puzzles when they have completed the normal exercises in a breeze.

One of the puzzle types uses a normal 0-6 domino set. Look at the figure in problem 1. In contrast to dominosa, the domino puzzle type most often used, the borders are clear, but the digits are missing.

Problem 1.^**/*****

The numbers along the sides are the sum of the pips in the respective rows and columns. It is up to you to figure out which domino should go where. Normal domino rules are followed: whenever two bones lay end to end, the numbers are equal.

For your convenience, here is a complete double 6 set:

You can check your solution here

Problem 2^**/*****

You can check your solution here

Problem 3^***/*****

You can check your solution here

A new puzzle is published at least once a month on the first Friday of the month. Additional puzzles may be published on other Fridays.

Billy’s Big Christmas Party

Billy was delighted to have gained entry to the Big Christmas Party in the neighbouring village. There were stalls and booths littered throughout the hall.

1) The apple pie stall^**/*****
The first stall he walked to showed delicious steaming hot pieces of apple pie on display. Several other kids had gathered in front of it.
A sign read:
4 and 7 give 33
3 and 2 give 5
8 and 5 give 39
A middle aged lady behind the stall held up two numbers: 6 and 3.
“This woman must be the wife of the math teacher,” he whispered to his neighbour.
The lady must have overheard him, because she laughed:
“Young man, I am the math teacher.”
But she was quickly satisfied when Billy quickly figured out the correct answer, collected his piece of apple pie and walked to the second stall.

You can check your solution here

2) The hot chestnuts stall^****/*****
The second stall displayed dishes of chestnuts filled with had chestnuts. A man was roasting the chestnuts on a small coal fire and serving them with several sauces.
A sign displayed some calculations:
11 + 11 = 8
12 + 59 = 18
18 + 47 = 16
23 + 39 = 16
He held up two numbers for the children in front of his table: 22 and 45.
Slightly softer than the previous time, Billy whispered to the girl besides him:
“Do they have two math teachers here?”
The girl looked at him saying:
“Did you ask if we have two math teachers here?”
The man heard it and laughed: “No, I’m the Arts teacher.”
Billy quickly grasped the problem and found the sum of 22 and 45.

You can check your solution here

3) The mince pies^****/*****
The third stall displayed a lovely looking plate with mince pies.
A piece of cardboard listed:
5 and 6 give 6
3 nd 7 give 7
7 and 8 give 8
She held up two cards showing 4 and 12. “What number do they give?” she asked. “I’ll tell you in advance the answer is not 12.”
To prevent him from asking, the girl besides him told him:
“No, she doesnt teach math. She teaches English.”

You can check your solution here

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.

Matchsticks – 3-1=8

1) 3-1=8?^***/*****
Please correct the following equation by moving two matchsticks:

You can check your solution here

New puzzles are published at least twice a month on Fridays.

Matchsticks patterns

What letter combination goes to the question mark?

You can check your solution here

If you like this puzzle, why don’t you have a look at my e-book?

Matchsticks – a diamond

Have a look at at this diamond – it is made up of 10 triangles.

Your challenges are:
1) 8 triangles^**/*****
Move 4 matchsticks and have 8 triangles

2) 7 triangles^**/*****
Move 4 matchsticks and have 7 triangles

3) 6 triangles^**/*****
Move 4 matchsticks and have 6 triangles

4) 5 triangles^**/*****
Move 4 matchsticks and have 5 triangles

You can check your solution here

New puzzles are published at least twice a month on Fridays.

River crossing

In the past I published several posts on river crossing puzzles. I think together they are the most extensive resource on river crossing puzzles on the web.

I used the week between Christmas and New Year to look for apps. To my surprise, there was just one, and it held just a few puzzles. Well, it did in spire me to:

1) The Autists and the Lazy.
Six people want to cross a river. They have a boat which can hold only 2 people at a time.
* Two of the six people are autists. They don’t want to be in the boat with any one else, though they don’t mind being on the same shore.
* Two of the people are outright lazy, and don’t want to row.
* The remaining two people are normal.
How many crossings does the boat have to make?

You can find the old posts here:
* Man, wife and kids – river crossing 1
* The farmer, the wolf, the goat and the cabbage – 2
* Three couples – river crossing – 3
* Bigamists – river crossing – 4

New brainteasers are published twice a month on Fridays.

You can check your solution here

100 doors challenge

Our daughter Margreet installed the “100 doors challenge” on her phone, and this weeks puzzles is based on one of the levels.

If 178 gives 237, what does 640 give?

You can check your solution here

New puzzles are published at least twice a month on Fridays.

Matchsticks – 3-7=8?

1) 3-7=8?^***/*****
Please correct the following equation by moving one matchstick:

1) 3-7=8?^***/*****
Please correct the following equation by moving exactly two matchsticks:

You can check your solutions here

Originally I had only puzzle nr. 2. I’d like to thank reader Mr. Haubrich for pointing out nr 1.

New puzzles are published at least twice a month on Fridays.

Happy new year!

What do you read when you superposition these three figures?

You can check your solution here

New puzzles are published twice a month on Fridays. Solutions are revealed one or more weeks later.

This puzzle was inspired by the “100 doors” app, and by the Dutch translation of 1000 casse-tete et enigmas by Piere Berloquin.