Tag Archives: Brainteaser

2020


It’s 2020, a new year! Here are a couple of 2020 related brainteasers:
1) 0-9!**/*****
Make each and every of the numbers 0-9 by combining the four digits 2, 0, 2, and 0 with arithmetic and mathematical operators. For example 0*(2+2)+0=0

2) two different digits**/*****
The year 2020 has only 2 different digits, 0 and 2. How many of those years do we have in this centur?

3) 0-9!**/*****
And as a sequel on 2): how many such years are there in this millennium?

You can check your solutions 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.

Bongard problem 39


Which rule satisfies the 6 figures on the left but is obeyed by none of the 6 figures on the right?
1)Bongard problem 10**/*****


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.

Numbers


1) Three blocks of numbers***/*****

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.

You can check your solution here

Math olympiad


Can you find a four digit number N that can be divided by 11, with the sum of the cubes of its digits is equal to N/11?

For example, 1342 / 11 = 122, but 1^3 + 3^3 + 4^3 + 2^3 = 1 + 27 + 64 + 8 = 100, which does not equal 122.

The problem is inspired by an old math olympiad question.

You can check your solutions here

A new puzzle is published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to discuss the puzzles, their difficulty level, originality and much more.

Bongard problem 36


Which rule satisfies the 6 figures on the left but not the 6 figures on the right?


The Russian scientist M.M. Bongard published a book in 1967 that contains 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 and at Harry Foundalis site, and in the category ‘Bongard problems’ in the right margin of this page.

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.

1 to 9


1 to 9 is the name of a twitter account linked to https://maththinkblog.wordpress.com/. It uses several puzzle formats, one of them is this:
fill in the digits 1 to 9 all exactly once in this square. The digit 4 has already been given. The numbers along side the square are the sum of the numbers in the diagonal, row or column.



You can check your solutions 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.

Geometry – or is it?


1) Three squares**/*****



On twitter I found the account of a very kind and smart lady called Catriona Shearer, who poses a lot of very nice and original math problems. One problem is reproduced here with her permission. In the figure above, the sides of the three squares are three consecutive integers. The length of the black line is 4√10.
What’s the total area?

You can check your solution here

2) Four squares***/*****
The puzzle above inspired me to the following puzzle:


The length of the sides of the three smaller squares are all natural numbers – integers if you prefer that term. The length of the side of the big square is 6√10.
What is the size of the three small rectangles?

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.

You can check your solution here

Add a nine to the end of the number


1) Adding a nine***/*****
22 = 4. Writing a 9 after it, I get 49 which is 72
42 = 16. Writing a 9 after it, I get 169 which is 132
What is the next square number, which, when adding a 9 after the number, is a square?

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.