Here’s a bonus puzzle inspired by a recent Christmas purchase.
I bought this jolly fellow in Covent Garden:
We named him Philbert, for some reason.
As you can see, Philbert has two cubes in his stomach (dice, basically), each of which has a digit on each face. By rearranging the dice, you can count the days until Christmas.
Puzzle 1 (EASY)
If we assume that both dice must be used at all times (i.e. 7 must be expressed as ’07’, as seen in the photo), what is the optimal way to paint the digits on to the dice such that Philbert can count down to 1 from the maximum possible number? What is that maximum number?
(I was pleased to see that the dice provided were indeed optimal!)
Puzzle 2 (A LITTLE LESS EASY)
What if Philbert had three dice? How should they be numbered and what would be the maximum number that Philbert could count down from?
Puzzle 3 (PRETTY CHALLENGING)
What if Philbert had n dice? What would be the maximum number he could count down from then?
Please submit your solutions via the comments below