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Sunday Times Teaser 3136 – Fill Cells Mentally, My Dear Watson

by Brian Gladman on October 28, 2022


by Stephen Hogg

Published Sunday October 30 202 (link)

Moriarty’s papers were alight. Holmes memorised a 3×3 grid of different 4-digit values in ascending order as illustrated, from A (lowest) to I (highest), noticing that one numeral wasn’t used. Three cells, isolated from one another (no corner or edge contact), held squares of squares. Three others, similarly isolated, held cubes of non-squares. The other three held squares of non-squares. Holmes told Watson these features, specifying only the lowest value. “Not square,” remarked Watson.

“True, and many grids match these facts. However, if I told you the positions of the squares of squares in the grid, you could deduce a majority of the other eight values (apart from the lowest one)” replied Holmes.

In ascending order, which values did Watson now know certainly?

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2 Comments Leave one →
  1. Brian Gladman permalink

  2. John Z permalink

    Slightly empirical solution in that I decided to discard one of the two possible configurations. This kept code length to a minimum.

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