61 equals 28?

Make the equation in the picture above correct. To do so, you may freely move the digits around. You may not add other stuff such as plus signs, multiplication signs, and so on.

Recently I purchased “Logic Brain Teasers”, published by Mensa. There was a puzzle on the back cover and while attempting to solve it as a family during dinner, the idea for this puzzle was born.

You can check your solution here

You are welcome to remark on the puzzle: its wording, style, level of difficulty. I love to read your solution times. Please do not spoil the fun for others by listing the solution.

I do offer my apologies that the puzzle above does not carry a christmas theme, as I had intended. I had two puzzles in mind, but in one I made an error in my calculation and for the other I had insufficient infomation on its origin.

Christmas time is something special in many parts of the world. For some, these are happy days with the family. For others, it’s just a few days off. For me, as an orthodox christian, it is a time of celebration.
Celebration, because where we humans develop irritation, dislike and even hate, God has come to offer a possibility of peace.
Celebration, becuase where we suffer poverty, He has come to share his richness with us.
Celebration, because where we suffer bondage, He has come to set us free.
Celebration, because the God, who is greater than our imagination can comprehend, chose to be born as a small and vulnerable baby.
I wish that you may enjoy the Christmas days and may experience a little bit of the peace, freedom, and richness he wishes to give us.

135

You never realized it. Even though I never met, I’m pretty sure of it. You never realized the number 135 is very special. That is because 1 + 3^2 + 5^3 = 135.
The question is: which three other three-digit numbers have this property?

You can check your solution here

Knights on a chessboard

In chess a knight may move 2 up/down and one sideways, or 2 sideways followed by one up/down. See the following illustration:

How many knights can you put on a normal 8×8 chessboard so that no knight may take another knight? And can you show that that is the maximum?

This problem was posted at the Dutch mathematics olympiad 1996.

You can check your solution here

How many numbers with a 5?

Quicky:
How many numbers between 1 and 999 contain a 5?

You can check your solution here

Two watches

I started two watches at the same time and found that one went two minutes an hour too slow and the other one minute an hour too fast, so that when I looked at them again the faster one was exactly one hour ahead. Can you figure out from from the picture at what time before noon the watches must have started?

This problem was first posted by American puzzle genius Sam Loyd. It was incorporated into his Cyclopedia of Puzzles on page 30.

You can check your solution here

You are welcome to remark on the quirks in the puzzle, and i especially welcome your solution times. The solutions itself will be published after one week.

Five triangles

Imagine a right triangle (formerly called a rectangled triangle). One side adjacent to the right angle is twice as long as the other. You will not find it very difficult to construct a square from 4 of these triangles.

But is it possible to construct a square from 5 of these triangles? And from 6? From 7?

These problems are derived from ‘doordenkertje’ 12 in the November 1969 issue of ‘Pythagoras’, a Dutch magazine in recreational mathematics. You will need some elementary geometry knowledge to solve this problem.

You can check your solution here

Pattern code – arrows

Here are some arrows, all different, and all labelled.

What should be the label of the arrow in the center?

You can check your solution here

A square

What is the smallest number of which the square ends with three identical digits? And indeed, 0 is excluded as a solution.
This is a slightly simplified version of a problem published as perplexity 466 by Henry Dudeney in The Strand magazine august 1919.

You can check your solution here

Rabbits and carrots

Here is a classic:
If 5 rabbits can eat 5 carrots in 5 minutes, how many carrots are eaten by half as many rabbits in half the time?

This kind of problem goes back to at least the middle ages. They have been formulated in many ways: slaves doing work, painters painting walls, cats catching mice, you name it.

You can check your solution here

Crossnumbers

Crosswords are among the worlds most printed and devised puzzles. And though they are puzzles with words, they are not language puzzles and they can be fairly easily generated once you have a large dictionary in electronic form available.

But Crosswords are so common place I have thus far avoided them in this blog. There are several number variants however, and the one presented here is geared towards math buffs.

Horizontal	Vertical
1 square with identical first and third digit 3 fibonacci number 5 perfect number 7 number of cards in bridge 9 happy number 10 catalan number 11 monodigit number 12 lucas number 14 happy number 16 narcistic number 18 circular prime 19 fibonacci number	1 factorial number 2 prime number 3 fourth power 4 catalan number 6 multiple of 11 8 third power 9 perfect number 12 third power and a square 13 fibonnacci number 15 triangular number 16 fermat prime 17 square

You can check your solution here