Teaser 3187

Wired Squares

Sitting at his study desk one morning, Ted noticed a paperclip poking out of his notebook, unbent to a straight thin wire. Opening it up he found that his granddaughter Jessica had drawn a square grid (less than 14cm side width) on one of the pages, with vertical and horizontal grid lines at 1cm intervals.

Musing this, Ted numbered each cell consecutively from 1, working left to right along each row from top to bottom in turn. Moving the wire over the page, he rested the wire over (or touching the corner of) some cells containing a square number. Placing the wire carefully, he was able to connect as many square-numbered cells as possible in this way. No square grid of less than 14cm side width could have allowed the connection of a larger number of squares.