Answer to Question #149823 in Combinatorics | Number Theory for Wesam

Question

An alien from the planet OMO Centauri writes the first ten prime numbers in arbitrary order as U,W, XW, ZZ, V, Y, ZV, ZW, ZY, and X. Each letter represents a nonzero digit. Each letter represents the same digit everywhere it appears, and different letters represent different digits. Also, the alien is using a base other than base ten. The alien writes another number as UZWX. Compute this number (expressed in base ten, with the usual, human digits).

Answer 1

First 5 prime numbers is 2,3,5,7,11

sixth prime number is 13

We have 5 numbers which have one letter

So Base could be only 12 - between 11 and 13

Next, we have 4 prime numbers with first letter Z

ZZ - should be 1*12 + 1 = 13

ZV, ZW, ZY is the next 3 prime numbers 17,19,23

17 = Z + 5

19 = Z + 7

23 = Z + 11

Hence V,W,Y - represents 5,7,11 in any order, the rest letter U is 3

Next, the last number XW - is 29

X*12+W = 2*24 + W = 29

Hence X is 2 and W is 5

So Z = 1, X = 2,U = 3 and W = 5

Answer: UZWX = 3152