Some playing cards are divided among A, B, C, D and E in such a way that A…

Concept

When a puzzle states only relative differences between quantities (more/less/equal), assign one variable to the quantity most statements refer to, rewrite every other quantity as that variable plus or minus a constant, and compare the constants -- the smallest constant offset identifies the smallest quantity, without needing to know the variable's actual value.

Application

Let the number of cards B receives be x. Translate each condition into an equation in terms of x:

1. "A gets one card less than B" gives A = x - 1.

2. "D and B get an equal number of cards" gives D = x.

3. "C gets 2 cards more than D" gives C = D + 2 = x + 2.

4. "E gets 3 cards more than B" gives E = x + 3.

Expressed in terms of x: A = x - 1, B = x, D = x, C = x + 2, E = x + 3. Comparing the constant offsets (-1, 0, 0, +2, +3), A carries the smallest offset, so A holds the fewest cards.

Cross-check

Substitute any value satisfying the conditions, say x = 10: A = 9, B = 10, D = 10, C = 12, E = 13. Ordering these -- 9, 10, 10, 12, 13 -- confirms A holds the least number of cards, matching the algebraic comparison.

Hence, A gets the least number of cards.