Sunday Times Teaser 3081 – Connect Four
by Howard Williams
Published Sunday October 10 2021 (link)
I have four different two-digit numbers, each having at least one digit which is a three. When I multiply any three of these numbers together I get a product that, with the inclusion of a leading zero, is one or more repetitions of the repetend of the reciprocal of the fourth two-digit number. A repetend is the repeating or recurring decimal of a number. For example 1 divided by 27 is 0.037037……, giving a repetend of 037; in that case, the product would be 37 or 37037 or 37037037 etc.
What, in ascending order, are the four two-digit numbers?