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 PageaDay 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 20160311 11:02:42 