WMC 2018 Senior Problem 5
Level
1
Suppose all 120 possible arrangements of the letters S, E, A, M and C are placed in alphabetical order. What is the “word”?
SEAMC
SECAM
SEACM
SAEMC
SAECM
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1 solution
The letters, in alphabetical order, are A, C, E, M, S, and there are 4 ! = 2 4 words beginning with each letter.
Therefore, the first 9 6 words in the list are all the words beginning with A , C , E , M which means that the 100th word is the fourth word beginning with S . Now we can list them in order: SACEM, SACME, SAECM, SAEMC. Therefore, the answer is SAEMC.