If FRIEND = 354768 and REFUND = 573968, how will TREND be written?

Concept

In a letter-coding problem, every letter is locked to one fixed digit. The reliable way to break the code is to read the letters that REPEAT across the given words: a repeated letter must take the same digit each time, which lets you pin those digits with certainty. A letter that appears only in the target word is new and simply takes a digit not already locked to any other letter.

Application

First pin the digits using the two given words by lining up letters with positions:

1. FRIEND = 354768 gives F=3, R=5, I=4, E=7, N=6, D=8.

2. REFUND = 573968 gives R=5, E=7, F=3, U=9, N=6, D=8.

3. The letters common to both words (R, E, F, N, D) get identical digits in each, so the mapping is consistent and can be trusted.

4. Now spell the target: T-R-E-N-D. The last four letters R, E, N, D are already pinned, in order, to 5, 7, 6, 8.

5. T is a new letter, present in neither given word, so it takes the smallest digit not yet locked to any letter; 1 is free, so T = 1.

6. Assembling T-R-E-N-D = 1-5-7-6-8 = 15768.

Cross-check

Two values share the ending 5768, so the deciding factor is the FIRST digit. A first digit of 3 would clash with F, which is already 3, so that value is ruled out. A first digit of 1 introduces no clash because 1 is unused. The values that scramble the 5-7-6-8 block break the fixed order the repeated letters must keep. Only 15768 satisfies every constraint.

Mapping used