Three slices of toast in a two-slice pan

Question

You have a pan that holds two slices of bread at a time and toasts one side of each slice in one minute. You have three slices and want both sides of all three toasted. The obvious plan takes four minutes: two slices for two minutes, then the third slice for two minutes. Do it in three minutes. Then say what the general rule is for n slices.

Accepted Answer

Three minutes. Call the slices A, B and C, each with sides 1 and 2. - Minute 1: toast A1 and B1. - Minute 2: toast A2 and C1. (B comes out half done; C goes in.) - Minute 3: toast B2 and C2. Every side has been toasted once, and the pan was full the whole time. Why three is optimal. Six sides need toasting, the pan does two per minute, so at least 6/2 = 3 minutes are needed. The schedule above achieves the bound, so it is optimal. The general rule. n slices have 2n sides; at two sides per minute that is at least n minutes, and n minutes always suffice: for even n toast pairs normally; for odd…

Three slices of toast in a two-slice pan

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