Maths Olympiad Prep

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, 2023

Number theory Difficulty 5.0 AIME, harder Find the answer United Kingdom

The number M=124563987M = 124563987 is the smallest number which uses all the non-zero digits once each and which has the property that none of the pairs of its consecutive digits makes a prime number. For example, the 5th and 6th digits of MM make the number 6363 which is not prime. NN is the largest number which uses all the non-zero digits once each and which has the property that none of the pairs of its consecutive digits makes a prime number. What are the 5th and 6th digits of NN?

(A) 66 and 33 (B) 55 and 44 (C) 55 and 22 (D) 44 and 88 (E) 33 and 55

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