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

*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?

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