# Sunday Times Teaser 3055 – Proceed to Checkout

*by Colin Vout*

#### Published Sunday April 11 2021 (link)

The dartboard at the Trial and Arrow pub is rather different from the standard one: there are only 3 sectors, each with a positive whole number label, and no central bullseye scoring region. There are still double and treble rings: for instance, if the sector label is 3, a dart in that sector can score 3, 6 or 9.

As usual, scores are counted down from a starting value, the idea being to finish (“check out”) by reaching exactly zero. Players take turns throwing three darts, or fewer if they check out before that. Unusually, the checkout doesn’t have to finish on a double.

The lowest impossible checkout is the smallest value that can’t be achieved in one turn; on this board that value is 36.

What are the sector labels?

with improvements from Frits and John Z (see below).

I’m a darts newbie but it strikes me that any score or ‘checkout’ that can be achieved with less than the maximum number of darts can also be achieved with the maximum number of darts (in this case 3) when the requirement to end on a double is relaxed. Consequently line 13 above can be simplified to:

Hi John,

Yes you are right, that can be simplified and it improves the

speed (not that speed matters much in this case).

Based on the generated code of my SubstitutedExpression program on S2T2.

Correction: b cannot be higher than 10.