A drawer holds 8 red socks, 6 blue and 5 green, and the light is off. Four socks are enough to be sure of a matching pair — and the eights and sixes have nothing to do with it.
You cannot list what you might pull out, so you count the worst that could happen instead. Three socks could be one of every color and still no pair; the fourth has to match one of them. Three colors, so four socks. A child who notices the counts never entered the argument has found the pigeonhole principle, which is the point of the page.
Why this sheet works
Then the sheet asks for a pair of a NAMED color, and now the counts are everything: the worst case is drawing every other sock in the drawer first, so it is all the others plus two. Both shapes are on the same page on purpose. "Colors plus one" is a rule that fits one of them, and a child who applies it without reading meets the question it does not fit.
Say how you know your number is always enough, however the picking goes.
1A drawer holds 10 red socks, 5 blue socks and 9 green socks, all mixed up. The light is off, so you cannot see what you are taking.How many socks must you take to be sure of a matching pair?Why
2A drawer holds 7 red gloves and 10 blue gloves, jumbled together in the dark.How many must you take to be sure of two red ones?Why
Worst-case puzzlesMedium drawers
Name: Date:
Say how you know your number is always enough, however the picking goes.
3A drawer holds 7 red gloves, 6 blue gloves and 12 green gloves, jumbled together in the dark.How many must you take to be sure of two red ones?Why
4A bag holds 5 red beads, 10 blue beads and 11 green beads. You reach in without looking.How many beads must you take to be sure two of them match?Why
Worst-case puzzles · Medium drawersAnswer key
1. There are 3 colors here (10 red, 5 blue and 9 green). The worst that can happen is taking one of each — 3 socks and still no pair. The next one has to match something, so 3 + 1 = 4. Notice the counts never came into it.2. The drawer holds 7 red gloves and 10 blue gloves. The worst that can happen is taking every other one first: all 10 of the others, and not a single red yet. Then two more must both be red, so 10 + 2 = 12.3. The drawer holds 7 red gloves, 6 blue gloves and 12 green gloves. The worst that can happen is taking every other one first: all 18 of the others, and not a single red yet. Then two more must both be red, so 18 + 2 = 20.4. There are 3 colors here (5 red, 10 blue and 11 green). The worst that can happen is taking one of each — 3 beads and still no pair. The next one has to match something, so 3 + 1 = 4. Notice the counts never came into it.
