A number is called abundant when its proper divisors — all its divisors except the number itself — add up to MORE than the number. Which of these is abundant?

Add the proper divisors in each case. For 15: 1 + 3 + 5 = 9. For 16: 1 + 2 + 4 + 8 = 15. For 18: 1 + 2 + 3 + 6 + 9 = 21. For 21: 1 + 3 + 7 = 11. Only 18 is beaten by its own divisors (21 > 18), so 18 is the abundant one; the other three fall short and are called deficient. Note how close 16 comes at 15 — every power of 2 misses by exactly 1, so no power of 2 can ever be abundant.