EDA Graffiti

Last week was the monkey puzzle. Monkeys go along a corridor shutting doors that are open and opening ones that are shut. It doesn’t take too much thought about this to realize that the doors left open will be those with an odd number of factors (and not just prime factors, all factors including 1). Almost all numbers have an even number of factors. If A divides N then N/A is also a factor, so they come in pairs. The one exception is perfect squares where both N and N/A are the same number so only get counted once. The third monkey doesn’t both open and shut door number 9 to take account of the fact that 3 is a factor of 9 twice over. So the answer is that the doors left open are the perfect squares, 1,4,9,16,25…961.

Today a country puzzle:

Name 9 countries that begin and end in A (in English). I’ll give you one just because it’s dubious: Antigua and Barbuda. You know the other 8 though. If you want a hint for another of the hard ones, watch the "Tour de France" today.

Here’s another country puzzle: pick a number from 1 to 10. Multiply by 9. Subtract 5. Add the digits. Add the digits again until you have a one-digit number. Whatever number that is, pick that letter of the alphabet (A=1, B=2 etc).

Now think of a country that begins with that letter.

Now think of an animal that begins with the last letter of that country.

What country is that animal from?

Australia. Oh, look, it begins and ends with A! Only 7 to go.