How did you get on with the hat problem? In case you got stuck there is a solution at the bottom of this post, but before we get to that, here’s this week’s puzzle.
We have all heard of the Reindeer first team: Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner and Blitzen, and Rudolph. They live with 90 others in 99 numbered stalls at the North Pole looked after by 100 highly trained elves, some of whom work at BOSS. Santa always picks his reindeer team in the following way.
At the beginning of the selection all the reindeer stall doors are closed and the elves draw lots. The elf who draws number 1 opens every door then the elf who draws 2 then closes every even door. Elf 3 then closes every open door/opens every closed door, whose number is a multiple of 3 and so on. When all 100 elves are finished, the Reindeer whose stalls are open are marched out for the honour of drawing the sleigh. It happens the same way every year and the first team always get selected. Which stalls do they live in?
Solution to the Hat Puzzle
Jodie agrees with the Elves that if she sees an odd number of red hats she will shout “RED” , while if she sees an even number of red hats she will shout “GREEN” (There are a LOT of Elves at the BOSS HQ Christmas party – it is the last fun they will have before Christmas Eve and they like parties, so Jodie has to shout pretty loudly!) The Elves know how many of them there are, though that is classified so I can’t tell you. Anyway, the elf in front of Jodie counts the number of red hats they can see in front of them and checks if it is odd or even. If that agrees with what Jodie told them with her cunning hat code then that elf knows they can see all the red hats that Jodie saw (there can be at most one difference) so they must have a green hat. Otherwise their own hat is red and either way they can call out the colour of their hat correctly. The other elves take note of whether that was red or green, updating the count of red hats that the next elf might see and so on. They all get their hat colours right, one at a time!