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.

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Areas


This week we have a plane and simple geometry problem

1) The rectangle**/*****


The rectangle contains three identical circles. The two smaller, shaded rectangle touch the sides of the rectangles and touch the circles. What percentage of the area of the large rectangle is covered by the two small rectangles?

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 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.

Bongard problem 35


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.

numbers 2, 3 and 5


A couple of years ago I posted the problem of four fours.

Recently I stumbled upon Gene Wirchenko’s Blog, and he had s similar problem.

Here is a variation of his problem. Combine 2, 3 and 5 to make all the numbers 0-22. Use each of the three digit exactly once, but you are free to use addition, multiplication, division, subtraction, brackets, exponentiation and factorial as often as you like.
For those of you who are not familiar with factorials a short reminder:
0! = 1
1! = 1
2! = 2*1
3! = 3*2*1
4! = 4*3*2*1
etc.

You can check your solution here

New puzzles are published at least twice a month on Fridays. Solutions are added after several weeks.