Each cell in the crossnumber is to be filled with a single digit.
A. 17
B. 16
C. 15
D. 14
E. 13
A. 17
Note that 1 across is a two-digit cube and therefore is 27 or 64. Also, 2 across is a two-digit square and hence is 16, 25, 36, 49, 64 or 81. Therefore 1 down must end with 1, 2, 3, 4, 6 or 8. If 1 across is 27, then the possibilities for 1 down are 21, 22, 23, 24, 26 and 28. Of these only 23 is prime. Alternatively, if 1 across is 64, then the possibilities for 1 down are 61, 62, 63, 64, 66 and 68. Of these only 61 is prime. So the two possibilities are that 1 across is 27, 1 down is 23 and 2 across is 36 or that 1 across is 64, 1 down is 61 and 2 across is 16. So the sum of the four digits in the crossnumber is 2 + 7 + 3 + 6 = 18 or 6 + 4 + 1 + 6 = 17. Of these two possibilities, only 17 is one of the options.
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