The letters E, G, H, I, N, S, T, V, and X represent different digits 0-9 (Neither S nor E is 0). SIX is a three digit number equal to the product of two consecutive integers, SEVEN is a five digit prime number, and EIGHT is a five digit perfect cube. What numbers are SIX, SEVEN and EIGHT?
Listed all 5 digit cubes and 3 digit n*(n+1) values
Eliminated all but number pairs that had the property that only the second digit was in common. These allowed only certain SEVEN values
10648 702 71x1y x,y = {3,9,5}
13824 930 91x1y x,y = {5,6,7}
32768 420 43x3y x,y = {1,5,9}
68921 380 36x6y x,y = {4,5,7}
Obviously, SEVEN values ending in 5 or an even value are not prime. This leaves ten values to be evaluated. Several are divisible by three and the other non-primes are not that hard to eliminate.
EIGHT SIX SEVEN
68921 380 36467
Approach and solution
