Maths Olympiad Prep

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Algebra Difficulty 5.7 AIME, harder Find the answer

6. A cryptanalyst has determined that the three most common trigraphs (blocks of length three) in a ciphertext are, LME, WRI and ZYC and guesses that these ciphertext trigraphs correspond to the three most common trigraphs in English text, THE, AND, and THA. If the plaintext was enciphered using a Hill trigraphic cipher described by CAP(mod26)C \equiv A P(\bmod 26), what are the entries of the 3×33 \times 3 enciphering matrix AA ?

A number or a short expression. Spacing and $ signs are ignored.

Solution

6. (2133123102537)\left(\begin{array}{cccc}2 & 1 & 3 & 3 \\ 1 & 23 & 10 \\ 25 & 3 & 7\end{array}\right)

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.