Enigma 100: Parkin in a cake-tin
18 June 2013
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From New Scientist #1244, 12th March 1981 [link]
Jessie makes parkin in a rectangular slab, but I store it in a round tin. She will make the rectangle in any proportions I specify. In the past I have specified 1 × 1 or 4 × 1. If it’s 4 × 1, I cut the slab in half and rearrange the two pieces as the sketch shows. In either case the proportion of the tin’s are filled is 2/𝜋: about 0.6366.
Parkin keeps best if the tin is as full as possible, and I have been wondering if I could improve on that proportion of 0.6366, by specifying a differently proportioned slab. Can you help me?
You can’t put one piece on top of another. And you are allowed only to make one straight cut in the slab before putting the pieces in the tin.
How many times the width of the slab should I ask Jessie to make its length?