## Teaser 2921: Octavia the octagonarian

**From The Sunday Times, 16th September 2018** [link]

Queen Octavia’s emblem was two concentric regular octagons (the outermost’s side length equal to the innermost’s distance between opposite sides). Seen from above her eightieth-birthday, level, cheesecake torte, with octagonal cavity all the way through and vertical side-faces, matched the emblem. Its outer side-faces were square and a two-figure whole number of inches wide. A four-feet diameter cylindrical cover protected it. At the party the whole torte was used, without wastage, to levelly fill a number of identical cuboid dishes (internally having length, width and depth, in inches, each a different single-figure whole number greater than one). Curiously, the number of dishes was a three-figure value with different numerals in descending order.

What was the torte’s volume in cubic inches?

[teaser2921]

## Jim Randell 9:22 am

on22 April 2019 Permalink |This Python program runs in 78ms.

Run:[ @repl.it ]Solution:The volume of the torte was 23,328 cubic inches.The outside faces of the cake are 18 inch squares, and this is the largest cake that will fit inside a 48 inch diameter tube.

There are 2 possibilities for the size of the serving dishes, either 972 dishes measuring 2×3×4 inches, or 432 dishes measuring 2×3×9 inches.

Although the larger dish size has a number of dishes composed of

consecutivedescending digits (which is possibly what the setter had in mind), I think the smaller sized dish makes the most sense. Which means there were almost 1,000 guests catered for.LikeLike