{"id":333,"date":"2011-03-15T07:01:06","date_gmt":"2011-03-14T23:01:06","guid":{"rendered":"http:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/?p=333"},"modified":"2024-02-16T21:13:46","modified_gmt":"2024-02-16T13:13:46","slug":"a-toasted-bread-puzzle","status":"publish","type":"post","link":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/2011\/03\/a-toasted-bread-puzzle\/","title":{"rendered":"A Toasted Bread Puzzle"},"content":{"rendered":"
\"What<\/a>
What shall I have on my toast?<\/figcaption><\/figure>\n

I have four different things I can spread on my toast. If I want to taste them all, I need four slices of toast.<\/p>\n

However, as we all know, the taste of jam on toast depends on what I had before. Jam after peanut butter tastes quite different from jam after vegemite<\/a>. So if I have 4 different things I can spread on my toast, how many slices of toast do I need, if I want to taste every combination of X after Y ?<\/p>\n

32 slices of toast will do the trick. There are 16 possible pairs of X after Y (Jam after jam, jam after peanut butter, jam after vegemite, jam after just margarine, and so on). Each pair has 2 slices of toast, so that’s 32 slices of toast.<\/p>\n

But the thought of eating so much toast makes my stomach feel queasy. Is there a way I can try every combination, but with less toast? How many slices of toast must I eat, what should they have on them, and in what order must I eat them, so that I get to try all 16 combinations of X after Y?<\/p>\n

By way of a hint, if I only have 2 things to spread, I can try all four combinations with only 5 slices of toast. I either eat<\/p>\n