[Guest]

Substitute each of the capital letters by a different base ten digit from 0 to 9 to satisfy this set of alphametic relationships. None of the numbers can contain any leading zero.

(RATTLE)/(LETTRA) = 64/37, and:

AT is a prime number

For an extra challenge, solve this puzzle without the aid of a computer program.

[superprismatic]

Rewrite as 37*RATTLE=64*LATTRA. Now, this can be rewritten again as

37*(10000*RA+100*TT+LE)=64*(10000*LE+100*TT+RA). This simplifies to

41104*RA=300*TT+71107*LE. Now, looking modulo 10, this becomes

4*A=7*E. So, we have the following relationship between A and E

(A is not allowed to be 0 by the OP):

When A is E must be
5 0
1 or 6 2
2 or 7 4
3 or 8 6
4 or 9 8

Since AT is prime, there are only 20 possibilities for the pair (A,T).

Each has a unique E which goes with it from the above table. So, we

only have 20 possibilities for the triple (A,T,E). Now for each of

these 20, we can find a relationship between R and L and get a list

of possible pairs (R,L). Plugging things back into the original problem,

we quickly find that the unique answer is R=4, A=9, T=7, L=2, and E=8.

Edited February 13, 2010 by superprismatic