Problem 43969. Sleeping Queens 1

Created by James

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My youngest daughter received a card game named Sleeping Queens for Christmas this year, and has been playing it nearly non-stop since opening it.You are dealt five cards, most of which have numbers 1-10 on them. There are other cards, but for now we will just deal with the numbers. You can discard cards in any of three different methods and draw that many new cards:<ul><li>Individual cards, one at a time</li><li>Pairs of cards, but not three or four of a kind</li><li>Cards that make up an addition problem.</li></ul>Write a MATLAB script that will tell you how how many different ways you can discard cards in your hand.For example, if your hand had the cards [1 2 2 4 9], you could discard<ul><li>Any of the cards individually (5)</li><li>The pair of 2s (1)</li><li>[2 2 4] because 2+2=4 (1)</li><li>[1 2 2 4 9] because 1+2+2+4=9 (1)</li></ul>so your script would output 8. Likewise, a hand of [1 2 2 2 6] would allow you discard cards 9 different ways:<ul><li>Any of the cards individually (5)</li><li>Any of the three different pairs of 2s (3)</li><li>[2 2 2 6] because 2+2+2=6 (1)</li></ul>So the output of your script for [1 2 2 2 6] should be 9. We don't need to know what the possible combinations are to discard just yet; we just need to know how many there are. Good luck, and happy hunting!

My youngest daughter received a card game named Sleeping Queens for Christmas this year, and has been playing it nearly non-stop since opening it.

You are dealt five cards, most of which have numbers 1-10 on them.  There are other cards, but for now we will just deal with the numbers.  You can discard cards in any of three different methods and draw that many new cards:

* Individual cards, one at a time
* Pairs of cards, but not three or four of a kind
* Cards that make up an addition problem.

Write a MATLAB script that will tell you how how many different ways you can discard cards in your hand.

For example, if your hand had the cards [1 2 2 4 9], you could discard

* Any of the cards individually  (5)
* The pair of 2s  (1)
* [2 2 4] because 2+2=4  (1)
* [1 2 2 4 9] because 1+2+2+4=9  (1)

so your script would output 8.  Likewise, a hand of [1 2 2 2 6] would allow you discard cards 9 different ways:

* Any of the cards individually  (5)
* Any of the three different pairs of 2s  (3)
* [2 2 2 6] because 2+2+2=6  (1)

So the output of your script for [1 2 2 2 6] should be 9.  We don't need to know what the possible combinations are to discard just yet; we just need to know how many there are.  Good luck, and happy hunting!

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Last Solution submitted on May 27, 2022

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Jean-Marie Sainthillier on 4 Jan 2017

Good problem

Rafael S.T. Vieira on 22 Jul 2020

Wouldn't [2 2 2 6] make a three of a kind?

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Problem 43969. Sleeping Queens 1

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