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