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From the people behind the Alan Turing Cryptography Competition.

Puzzle 6

There is just one slice of Chef Jean's signature banoffee cake left! The remaining slice is from the corner of a large square cake; it consists of a cuboid of banana cake 4cm high, 8cm wide and 5cm deep, covered on top by a 2cm-thick layer of toffee icing, and with 1cm and 1.5cm thick layers of icing on two sides, so that the entire slice is a cuboid 6cm high, 9cm wide and 6.5cm deep.

Uniformly sprinkled over all three iced faces of the slice is an infinitely thin (but infinitely delicious) dusting of cocoa powder.

Schematic of the cake

Jean wishes to cut the slice into two equal pieces — equal in the sense that each has the same volume of cake, the same volume of icing, and the same area of sprinkled cocoa powder — using a single planar cut. At what angle to the vertical must the knife be inclined, in order to make this cut?

Give your answer in degrees, to two decimal places.

This problem was first solved on Wed 24th February at 4:40:10pm
Mathsbombe Competition 2021 is organised by the The Department of Mathematics at The University of Manchester.
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