# Sunday Times Teaser 3123 – A Six-Pipe Problem

*by Nick MacKinnon*

#### Published Sunday July 31 2022 (link)

A factory makes six types of cylindrical pipe, A to F in decreasing size, whose diameters in centimetres are whole numbers, with type A 50 per cent wider than type B. The pipes are stacked in the yard as a touching row of As with an alternating row of touching Bs and Cs in the next layer, with each B touching two As. Type Ds fill the gap between the As and the ground; Es fill the gap between As and the Bs; and Fs fill the gap between As, Ds and the ground. Finally another row of As is put on top of the stack, giving a height of less than 5 metres.

What is the final height of the stack in centimetres?

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