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Form 21 n Times (Posted on 2016-03-11) Difficulty: 2 of 5
The array below represents a set of 16 playing cards, with the A's representing Aces:

A 3 5 8 10 2 4 9 4 2 7 A 2 5 3 8

Divide the array into sections of adjacent cards so that the sum of the cards' values in each section will be 21. Each Ace can represent either 1 or 11 and you must determine how many sections are needed.


From Page-a-Day Calendar 2016: Amazing Mind Benders, by Puzzability (Mike Shenk, Amy Goldstein and Robert Leighton), Workman Publishing, NY; puzzle for March 9.

See The Solution Submitted by Charlie    
Rating: 4.0000 (1 votes)

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Solution Solution spoiler Comment 2 of 2 |
The sum without the aces is 72.  The sum with {0,1,2} elevens is {74,84,94}.  84=21*4 so one of the aces is a one the other is eleven and there are four regions.  It's not hard to see the lower one can't be the eleven.  

<center>     A   3   5 | 8
--- --- 10 | 2 | 4 9
--- --- --- 4 | 2 7 A
--- 2 5 | 3 8
</center>

Edited on March 11, 2016, 11:03 am

Drat the formatting died.  The upper A joins with 3,5,3.  The 10 reaches down to 4,2,5.  The lower right is 3,8,A,7,2.  Upper right is 8,9,4.

Edited on March 11, 2016, 11:05 am
  Posted by Jer on 2016-03-11 11:02:42

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