Sunday Times Teaser 3164 – Touching Base
by Andrew Skidmore
Published Sunday May 14 2023 (link)
Liam has a pack of twenty cards; each card has a number printed on it as a word rather than figures.
There are two cards with ONE, two cards with TWO etc, up to two cards with TEN. He has taken four of the cards to construct an addition sum. The largest value card he has used is the sum of the values of the other cards, eg, ONE + ONE + TWO = FOUR.
If I now work in the base equal to that sum (ie, base 4 in the example), and consistently replace letters with single digits, this gives a correct sum. All of the possible digits in that base are used.
Leaving the answer in the working base, what is the total of my addition sum?