Sunday Times Teaser 3028 – Rainbow Numeration

by Stephen Hogg

Published Sunday October 04 2020 (link)

Dai had seven standard dice, one in each colour of the rainbow (ROYGBIV). Throwing them simultaneously, flukily, each possible score (1 to 6) showed uppermost. Lining up the dice three ways, Dai made three different seven-digit numbers: the smallest possible, the largest possible, and the “rainbow” (ROYGBIV) value. He noticed that, comparing any two numbers, only the central digit was the same and each number had just one prime factor under 10 (different for each number).

Hiding the dice from his sister Di’s view, he told her what he’d done and noticed, but wanted her to guess the “rainbow” number digits in ROYGBIV order. Luckily guessing the red and orange dice scores correctly, she then calculated the others unambiguously.

What score was on the indigo die?