more socks

Originally posted by biffo konker
I have 3 boxes of socks.1 box contains white socks,another black and the third contains both black socks and white socks.All the boxes were correctly labelled with what socks were inside but my son switched all the labels round and challenged me to re-label all 3 boxes correctly,by picking just one sock from just one box.Which box should i choose from.I am not allowed to look inside.

are we to assume that no box now has its correct label? because otherwise there would be no way to know for sure with only one pick which box you are really pulling from (the single color or the both color box)

if it is to be assumed that no box currently is wearing its correct label, then pick a sock from the "both" box. if you get white, that box should be labeled "white" (WLOG the same argument can be used for black). now, the box you took the "white" label from cannot be the "both" box because then the 3rd box would have its original (in this case "black"😉 label from before junior's "switcheroo," which contradicts the assumption we made to begin this whole line of reasoning. so, the box you removed the label from is in fact the "black" box, and the one that was labeled "black" is really the "both color" box.

again, the same line of reasoning can be followed switching the words "black" and "white" through that whole paragraph.