Queries

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Electronics & Computer Science Department
IITR

sQuieeez -1 13th Feb 08

Answers to the sQuieeez 1 problems are :

Answer 1:

3468

Starting at any of the N's, there are 17 different readings of NAK, or 68 (4 times 17) for the 4 N's. Therefore there are also 68 ways of spelling KAN. If we were allowed to use the same N twice in a spelling, the answer would be 68 times 68, or 4,624 ways. But the conditions were, "always passing from one letter to another." Therefore, for every one of the 17 ways of spelling KAN with a particular N, there would be 51 ways (3 times 17) of completing the NAK, or 867 (17 times 51) ways for the complete word. Hence, as there are four N's to use in KAN, the correct solution of the puzzle is 3,468 (4 times 867) different ways.

Answer 2:

Note that ≠ if and only if n = m² + m for some m. Thus n + and n - each increased by 1 except at n =m² + m, where the former skips from n = m² + 2m to n = m² + 2m + 2 and the latter repeats the value m². Thus the sums are

= 2 + 1 = 3.