Question

Tim has 74 socks, that are white or black. He has 1 more pair of white socks than black socks. How many individual socks of each color does he have?

He has
black socks and

white socks.

Answer 1

Let W = white socks, B = black socks. Pairs of white = floor(W/2), pairs of black = floor(B/2). We are told floor(W/2) = floor(B/2) + 1 and W + B = 74.

Write W = 2a + r_w, B = 2b + r_b with r_w,r_b ∈ {0,1}. Then a = b + 1 and
4b + 2 + r_w + r_b = 74 → 4b + (r_w + r_b) = 72.
The only way is r_w = r_b = 0 and b = 18, so
B = 2b = 36, W = 2(b+1) = 38.

He has 36 black socks and 38 white socks.