In the following table, each row of P, Q, and R are a set of numbers for which

P³ + Q³ + R³ = P_Q_R

where P_Q_R is composed of the digits of P, Q, and R put together.
For example, 4³ + 18³ + 33³ = 41833.

In this puzzle, however, P, Q, and R are each two digit numbers.
Also, there are no zeroes in any of the variables.

     P        Q        R    
     a        k        j
    a/2      c/4       n
     b        c    2(h+j/4)/a
    j/4      2g/7     3a/4
     2m       f       e/31
     2m      j/2      d/37

The grid below contains all the variables in the table, where a1 is the first digit of a, a2 is the second digit of a, etc, and where a1 and b1 (being in the same box of the grid) are the same digit.

 ___________________
| a1 | a2 | c1 | c2 |
| b1 |    | d1 | f1 |
|----|----|----|----|
| e1 | e2 | e3 |    |
| b2 | h1 | d2 | f2 |
|----|----|----|----|
|    | g1 | g2 | g3 |
| k1 | h2 | d3 | n1 |
|----|----|----|----|
| j1 | j2 | m1 | m2 |
| k2 | h3 |    | n2 |
 ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ

Complete the grid from the given information.

(In reply to SOLUTION by rerun141)

... almost like cheating :-)

but clever use of the repeated number in list (98), and kudos for solving the problem!

Posted by SilverKnight on 2003-12-19 11:14:32