Mathturion

The Quaestor’s Trial of Numbers

“Many men claim mastery over numbers, yet few are fit to guard the coin and ledgers of Rome. Therefore do I set before thee a trial, that I may judge whether thy mind be worthy to serve among my rationarii. Before thee stand nine sacks of grain, each marked with a number. Behold how 28, when multiplied by its neighbouring 7, doth yield 196 — as is shown upon the middle sacks. Yet the other pair, 34 and 5, fail to produce that selfsame sum. I charge thee now: move as few sacks as may suffice, so that both pairs, each multiplied by its neighbour, shall render equally the number inscribed betwixt them. He who accomplisheth this task with wisdom and swiftness shall prove himself worthy of a place within the Imperial Treasury.”

Nine sacks bear the digits 1–9. Dispose them such that left × pair = middle = pair × right. The solution is unique and may be reached in no more than 3 moves.

Click a sack to select it (highlighted in gold), then click another sack to swap them. Click the same sack again to deselect.