Question

☆☆A small number of cards has been lost from a complete pack. If I deal among four people, three cards remain. If I deal among three people, two remain and if I deal among five people, two cards remain. How many cards are there?☆☆

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Answer 1

In other words, the number of cards “n” is given by:

4p + 3 = n

3q + 2 = n

5r + 2 = n

This is three equations in four unknowns, so this cannot be solved algebraically for a unique solution. However, because there are bounds on the value of “n” (more than zero, somewhat less than 52), you can work numerically.

For instance, let’s put a floor on “n” of 40. Then:

4p + 3: 43, 47, 51

3q + 2: 44, 47, 50

5r + 2: 42, 47