# Sunday Times Teaser 3084 – Face Value

*by Susan Bricket*

#### Published Sunday October 31 2021 (link)

Plato: I have written a different whole number (chosen from 1 to 9 inclusive) on each of the faces of one of my regular solids and have labelled each vertex with the product of the numbers on its adjacent faces. If I tell you the sum of those eight vertex labels, you can’t deduce my numbers, but if I rearrange the numbers on the faces and tell you the new sum, then you can deduce the numbers.

Eudoxus: Tell me the new sum then.

Plato: No, but I’ll tell you it’s a 10th power.

Eudoxus: Aha! I know your numbers now.

Plato: Yes, that’s right. But if I now told you the original sum, you couldn’t work out which numbers were originally opposite each other.

What was the original sum?

@Brian,

Is there any reason why you prefer to use math.pow over **?

I also was expecting a check on uniqueness of used digits for all fpts entries (around line 26)

@Frits, No particular reason for my use of pow().

The construction of face pair triples ensures that they have no duplicated digits.

My first programme did some unnecessary computations, and I was never happy with it. This one works more directly.