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.

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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.

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