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

If you’re interested in our book on the Maths of Christmas, it’s available by clicking on the image. US edition here.