Question

If G, M, equals, 12GM=12, find G, KGK.

Answer 1

I’m not sure I understand the notation. A couple of clarifying questions:

- Do letters G, M, K stand for digits (0–9) or for variables that can be any number?
- What exactly does "12GM = 12" mean? Possible readings:
- GM = 12 (G times M equals 12)
- 12·G·M = 12 (twelve times G times M equals 12)
- the four‑digit concatenation "12GM" equals 12 (which would be impossible)
- What is "KGK"? Is that the three‑digit palindrome with digits K,G,K (concatenation), or the product K·G·K?

If you confirm which you mean I’ll solve it. Meanwhile, here are the likely interpretations and their answers:

1) If GM = 12 means G·M = 12 and G,M are (positive) digits (1–9):
- Possible (G,M) pairs are (2,6), (3,4), (4,3), (6,2).
- Without more info, G could be 2, 3, 4, or 6.
- If KGK denotes the three‑digit palindrome with outer digit K and middle digit G, then for each possible G there are 9 possibilities for K (1–9) giving palindromes K G K (e.g. for G=3: 131, 232, 333, …, 939).

2) If 12·G·M = 12 (i.e. 12GM = 12 as a product), then G·M = 1, so with integer digits the only solution is G = 1, M = 1. Then KGK depends on K as above.

Tell me which interpretation you intended (or give the exact original problem text) and I’ll give the precise solution.