# Sunday Times Teaser 2921 – Octavia the Octagonarian

*by Stephen Hogg*

#### Published September 16 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?