Logic & numbers
Black and white socks. A dark drawer. How many draws guarantee a color match?
Three draws. Two colors can give you two different socks; the third must match one. Assume enough socks are available.
The answer
Three draws. Two colors can give you two different socks; the third must match one. Assume enough socks are available.
The idea
A guarantee must survive the least convenient possible sequence.
An example
Extend the drawer to three colors, with enough socks available. You could draw one of each before getting a match, so the fourth guarantees a repeated color. The reasoning counts categories and then adds one.
Try it
Try the same reasoning with four colors. Explain why one fewer draw cannot guarantee a match.
More context
In the worst case the first two have different colors. The third must match one. Assume there are enough socks and color alone defines a pair.
the 102 platform · Constructed puzzle