Problem 2318. Combine Cards to make 21

Created by James Kristoff

Solve Later

Given between two and six cards, e.g.

 A _ 3 _ 7 _ 6 _ 2

place one of the mathematical symbols (+,-,*,/) in the space between each pair of cards to make the equation equal 21.

The input will be a string, e.g.

'A3762'

The output should be a cell array of mathematical symbols in the order that satisfies the puzzle, e.g. for the string given above, the output would be:

{'+-*/'}

Which means that A + 3 - 7 * 6 / 2 = 21.

A + 3 = 14
14 - 7 = 7
7 * 6 = 42
42 / 2 = 21

Rules:

The Ace can represent either 1 or 11.
All operations should be performed from left to right
Cards will be represented by the characters: A,2,3,4,5,6,7,8,9,J,Q,K

Solve

Solution Stats

Last solution submitted on Jul 03, 2019

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Alfonso Nieto-Castanon on 14 May 2014

nice problem!, consider perhaps adding 'AAA' (with solutions {'+-','-+'}) to the testsuite to make it more challenging

James Kristoff on 16 May 2014

Thanks for the suggestion Alfonso. That does make things a little more challenging. :)

J.R.! Menzinger on 19 May 2014

Did you have fun this this last test case, isn't it?? XDDD

YOU... BAD GUYS!! ;-)

Solution Comments

Solution 444970

2 Comments

2 Comments

Marco Castelli on 22 May 2014

Probably I don't understand what problem ask, but...I think test suite is wrong. For example: test suite 2.
cards = 'A23QJK';
mathSymbols = {'+-/++'};
1+2=3-3=0/9=0+8=8+10=18 that is not 21!
I found {'+-+-+','+/*--','-+-++','-*/++'}=21.
I've problem even in test 5

Alfonso Nieto-Castanon on 22 May 2014

'A' can take the value 1 or 11 (e.g. 'AAA' with symbols '+-' means 11+11-1==21). 'JQK' all count as 10 (e.g. 'A23QJK' with symbols '+-/++' means ((11+2)-3)/10+10+10==21)