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Form 21 n Times II (Posted on 2016-08-11) Difficulty: 2 of 5
The array below represents a set of 16 playing cards, with the A's representing Aces:

A 5 5 A 5 2 4 10 3 8 7 4 A A 2 6

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 August 6,7.

  Submitted by Charlie    
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Solution: (Hide)

If all four Aces were valued at 1, the total of the array would be 65. We can add one, two, three or four times 10 by considering one through four aces as being 11. Only 65 + 4*10 is a multiple of 21, that is, 105 = 5*21, and so there are five sets each of which adds to 21 and each Ace counts as 11.

The only possible division of the array is:


 A   5   5 | A
---+---+---+
 5   2 | 4 |10
   +---+   +---
 3 | 8 | 7   4
   +   +---+
 A | A   2 | 6

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre(2): Full solution - SPOILERAdy TZIDON2016-08-11 10:45:09
solutionDaniel2016-08-11 09:47:46
Some ThoughtsPossible solutionbroll2016-08-11 09:40:11
re: Full solution - SPOILERCharlie2016-08-11 09:06:28
SolutionFull solution - SPOILERAdy TZIDON2016-08-11 08:29:55
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