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Sunday Times Teaser 3084 – Face Value

by Brian Gladman on October 30, 2021

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?

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5 Comments Leave one →
  1. Brian Gladman permalink

    • Frits permalink

      @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)

      • Brian Gladman permalink

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

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

  2. Erling Torkildsen permalink

  3. Erling Torkildsen permalink

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

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