I
have been stressing over this one cryptarithm. Can you
help me solving it? |

hi * nt ------ at fin ------ foot If "t" in the multiplier times "hi" in the multiplicand yields "at" in the first partial product; also "n" in the multiplier times "hi" in the multiplicand yields "fin" in the second partial product, this suggests that i = 1 or otherwise i = 6 and "t" and "n" are even numbers. Letīs first try i = 1. Substituting "i" for "1" the set-up would become: h1 * nt ------ at f1n ------ foot Easy to see that "o" should equal 2 because it results from "1" plus a "carry 1" from the sum a + n = o + 10. So we come to: h1 * nt ------ at f1n ------ f22t In order to get "n" times h1 = f1n we must have n = 3 and h = 7 or otherwise n = 7 and h = 3. And in both cases "f" should equal 2. But this is impossible because we have already determined o = 2. Hence we must go back to where we started and now make i = 6 as far as i = 1 has revealed impossible. Then we start again with: h6 * nt ------ at f6n ------ foot We also know that "t" and
"n" are even numbers. Easy to deduct that h6 * nt ------ In the column printed with characters
in bold we see that a + n = 17. For this to be true there
are only two alternatives: 9 + 8 = 17 or 8 + 9 = 17. But
we also know thar "n" is an even number, so
that makes h6 * 8t ------ 9t f68 ------ f77t In the first partial product we see
that "t" times "h6" equals
"9t". Hence 46 * 82 ------ 92 f68 ------ f772 It is evident that f = 3 leading us to the final solution: 46 * 82 ------ 92 368 ------ 3772 The section "EXAMPLES WORKED OUT IN DETAIL BY MASTER PUZZLISTS" contains 6 puzzles solved step-by-step by renowned puzzlists, where you can learn many basic tips for problem-solving. |