by Andrew Skidmore
Published Sunday November 01 2020
I noticed a dartboard in a sports shop window recently. Three sets of darts were positioned on the board. Each set was grouped as if the darts had been thrown into adjacent numbers (eg, 5, 20, 1) with one dart from each set in a treble. There were no darts in any of the doubles or bulls.
The darts were in nine different numbers but the score for the three sets was the same. If I told you whether the score was odd or even you should be able to work out the score. The clockwise order of numbers on a dartboard is:
20 1 18 4 13 6 10 15 2 17 3 19 7 16 8 11 14 9 12 5
What was the score that all three sets of darts made? [i.e. that made by each set of three darts]
Sunday Times Teasers Discussion Group 
This a gentle teaser. I found the solution by looking for odd and even totals. I then found a shorter route.
Thanks John. I read this one before going to bed, and woke up this morning realising what the shorter route would be. So a very quick solution.
When one parity, by inspection, soon revealed multiple solutions and the other parity only came up with three cases to check, the answer was not hard to find.
I suspect the proudest route to the solution is all about how to deduce what parity it must have.
After the solution was found, I did amuse myself by modelling the teaser in GeoGebra. It merely visualizes and facilitates inspections rather than provide a solution. The model is available here.
Hi Erling
Your model is ingenious, but too complicated. You only need to consider the cases where one dart from each set is a treble, i.e. 3 tries for each set of 3.
best regards
Thanks, Robert. I must write that flaw on the account for poor knowledge of dart jargon. As the doubles and bulls were explicitly excluded in the text, I was left with “number” to be a single or triple score (and took “treble” to somehow refer to the number of arrows).
I got a warning that something was wrong when I read Nicky’s comment this morning..
Yes, it’s bad practice for authors to assume we have knowledge of jargon peculiar to a particular sport. Treble is an interesting word, in English it’s often used as an alternative to triple (both from the same Latin root), but it has other specific meanings. In music it usually indicates the highest pitch – e.g. treble recorder. But treble singers are usually boys, as opposed to female sopranos who sing the same notes. Hi-fi tone controls are always bass & treble – and so it goes on. My online dictionary gives ‘Tredoble’ as a Norwegian equivalent, but I don’t know if that includes the alternative meanings . . .
Yes, “tredoble” is “to multiply by three”, a verb composed by “three” and “double” (not perfect logic!). As a noun it becomes “tredobling”, and that fits the use of “treble” in the text. So I just wasn’t careful, and jumped into conclusions. If that had left the teaser with no unique solution, I would have been forced to read the text more carefully. But regretfully it did not affect the solution.
Committed darters in Norway no doubt use the English word.
Seemed a silly teaser to me…
Robert
It’s a speed test – waking up at 6am on Saturday, i did it (by hand) in less than the 3 minutes it took for my kettle to boil . . .
Solutions to earlier teasers placed on this site are now available on our Solutions page.
I didn’t really look for a shortcut as the long route doesn’t take much time or paper. For each set of three board segments calculate the 3 possible totals. Look for totals that can be made in at least three different ways using at least 9 segments of the board, three totals comply. Two of the totals have one parity. The other total with the other parity is the answer.