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Sunday Times Teaser 3020 – Baz’s Bizarre Arrers

by Stephen Hogg

Published Sunday August 09 2020 (link)

“Bizarrers” dartboards have double and treble rings and twenty sectors ordered as on this normal dartboard. However, a sector’s central angle is [100 divided by its basic score]°. The 20 sector incorporates the residual angle to complete 360º.

Each player starts on 501 and reduces this, eventually to 0 to win. After six three-dart throws, Baz’s seventh could win. His six totals were consecutive numbers. Each three-dart effort lodged a dart in each of three clockwise-adjacent sectors (hitting, in some order, a single zone, a double zone and a treble zone). The three-sector angle sum (in degrees) exceeded that total.

The sectors scored in are calculable with certainty, but not how many times hit with certainty, except for one sector.

Which sector?

7 Comments Leave one →
  1. Brian Gladman permalink

  2. Frits permalink

    Hi Brian,

    If the six totals had come out as 54-59 the score after six three-dart throws would have been 339 leaving a 162 which is not a finish at darts.

    Should “sum(t6) + 300 >= 501” not have been at least “sum(t6) + 170 >= 501”?

  3. Brian Gladman permalink

    Hi Fritz,

    Yes, the 300 is wrong. I don’t know much about darts and I thought that the bull was worth 100 but I have since discovered that it is 50. So the highest three dart score is 180, not 300 as I first thought (now corrected).

    The purpose of that bit of code is not to allow only those three dart scores that can be finished with a seventh three dart score through but rather to prevent those going through that definitely cannot be finished in this way.

    To only allow scores through that can be finished with a seventh three dart throw would require eliminating scores that require an impossible three dart score to finish and this is more work than I believe is necessary to compute the teaser’s solution.

  4. Frits permalink

    170 is the highest finish as you have to end with a double!

    PS I noticed you used a lot of tuples, do you use them iso lists and sets because they are immutable?

  5. Brian Gladman permalink

    Hi Frits,

    I fear I have had to delete your comments after this post since the difficulties you are having in posting formatted text makes them very messy. It is also difficult to understand their relevance since the exact details of the seventh throw are not needed to solve the teaser because other constraints lead to a single solution.

    As you have found, this site does NOT use <code> and </code> tags – it uses <pre> and </pre> tags which default to Python code. If you want to post formatted text other than in Python you need to use tags of the form <pre lang=”language” > … </pre> where “language” is that which you want to use. The full details are available here.

  6. Frits permalink

    Thanks Brian, I thought I could use the code button.

    I just wanted to add a small analysis.

    The lowest finish is 2 (as ending up with 1 leads to a “no score”).

    Among others the 169, 168, 166, 165, 163, 162, 159 condition is relevant to the teaser as otherwise the code may report an incorrect answer (meaning Baz can’t finish in the 7th throw) if the code reports multiple solutions.

    It is not important that the code handles every requirement but what is good practice is to verify afterwards that all (non-coded) requirements have been met.

  7. Tony Smith permalink

    For what it is worth, the description of the game does not require a finish to be on a double.

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