Let capitalised letters of the alphabet stand for 4-digit prime numbers each of whose digits is distinct and also prime, so that e.g. A=5237.

A pair of such letters stands for the concatenation of two such numbers to form an 8-digit number, e.g. AA=52375237

Denote 8 different such 4-digit primes by the letters of the word CAPTURES, so that each of CP,ET,PU,RU,TE,TR, and UC is also prime.

Given that A=5237, what is the value of S?

answer:  S=2753

S o l u t i o n :

  the choices for letters are: 2357,2753,3257,3527,5237,5273,7253,7523.<br>

5237 is A, so we try pairs-combinations out of the remaining 7 four digits numbers.
  Using a prime/composite applet 8 eight digit numbers qualify, only two  of them 23573522  & 35222357 fit the TE-ET format. 

CAPTURES==><br>
 

C=3257<br>

     A= 5237(KNOWN)<br>

P= 5273 <br>

T= 2357<br>

U=7253<br>

R=7523<br>

E=3527<br>

So S  IS  left unassigned with only one fourtuple left i.e  2753<br>

s=2753  

Truly beautiful & surprising problem.  Like!!

 

Edited on June 14, 2011, 7:51 pm

Posted by Ady TZIDON on 2011-06-14 13:02:14