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Given 26 constants labelled A to Z, let $A = 1$.

The rest of the constants have values that are equal to the position of that letter in the alphabet, raised to the power of the previous constant, so:

  • $A = 1$
  • $B$ (the letter in the second position) $= 2^A = 2^1 = 2$
  • $C$ (the letter in the third position) $= 3^B = 3^2 = 9$
  • etc.

Find the exact numerical value for this expression:

$(N-A) * (N-B) * (N-C) * ... * (N-Y) * (N-Z)$

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What do you mean with $N$? If it is a letter, then $0$ – Ilya Jun 8 '11 at 16:35
Well... the expression includes (N-N), does it not? – mixedmath Jun 8 '11 at 16:41

For the sake of having an answer: the expression is multiplied by the term $(N-N)$, which is zero, so the whole thing evaluates to zero.

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This actually appears on Math Overflow under the question "Math Puzzles for Dinner."

Here is the link.

There is an answer there too, but my hint is what happens around the letter $M$ in the product?

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