Mathematics
Intermediate Mathematical Challenge
2023
10

10

Eight of the digits from 0 to 9 inclusive are used to fill the cells of the crossnumber. What is the sum of the two digits which are not used?

‍

A. 12

B. 13

C. 14

D. 15

E. 16

Answer

D. 15

SOLUTIOn

There is only one two-digit power of 6, namely 36, so 1 down is 36. Also, there is only one four-digit power of 5, namely 3125.

Therefore 1 across is 3125. There are two four-digit powers of 4, namely 1024 and 4096.

However, we know from 1 down that the units digit of 2 across is 6, so 2 across is 4096.

Hence the only two digits which do not appear in the completed crossnumber are 7 and 8. Their sum is 15.

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