Mathematics
Grey Kangaroo
2023
8

8

Theodorika wrote down four consecutive positive integers in order. She used symbols instead of digits. She wrote the first three integers as □ ♢ ♢, ♥ △ △, ♥ △ □. What would she write in place of the next integer in the sequence?

A ♥ ♥ ♢ B. □ ♥ □ C. ♥ △ ♢ D. ♥ ♢ □ E. ♥ △ ♥

Answer

E.

SOLUTIOn

Since the first symbol changes from the first to the second integer, we know the hundreds digit must have changed. Therefore ♢ = 9, △ = 0 and ♥ = □ + 1. Also, since the last digit of the third integer is □, we know that □ = 1 and hence that ♥ = 2. Therefore the next number would be 202, which she would write as ♥ △ ♥.

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