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Neat Aten (Posted on 2009-09-26) Difficulty: 3 of 5
Substitute each of the capital letters in bold by a different base ten digit from 0 to 9 to satisfy this set of alphametic relationships. None of the numbers can contain any leading zero.

  • NATE is divisible by 3, and:
  • ATEN is divisible by 7, and:
  • ANTE is divisible by 11, and:
  • NEAT is divisible by 17.
What are the possible value(s) that NEAT can assume?

See The Solution Submitted by K Sengupta    
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Solution with computer Comment 3 of 3 |

The two sets of values followed by lines with their values mod 3, mod 7, mod 11 and mod 17:

 9270  2709  2970  9027
 0  0  0  0
 2  0  2  4
 8  3  0  7
 5  6  12  0

 9417  4179  4917  9741
 0  0  0  0
 2  0  3  4
 1  10  0  6
 16  14  4  0

FOR a = 1 TO 9
 used(a) = 1
FOR n = 1 TO 9
 IF used(n) = 0 THEN
   used(n) = 1
FOR t = 0 TO 9
 IF used(t) = 0 THEN
   used(t) = 1
FOR e = 0 TO 9
 IF used(e) = 0 THEN
   used(e) = 1

nate = n * 1000 + a * 100 + t * 10 + e
neat = n * 1000 + e * 100 + a * 10 + t
ante = a * 1000 + n * 100 + t * 10 + e
aten = a * 1000 + t * 100 + e * 10 + n
IF nate MOD 3 = 0 THEN
  IF aten MOD 7 = 0 THEN
  IF ante MOD 11 = 0 THEN
  IF neat MOD 17 = 0 THEN
   PRINT nate; aten; ante; neat
   PRINT nate MOD 3; aten MOD 3; ante MOD 3; neat MOD 3
   PRINT nate MOD 7; aten MOD 7; ante MOD 7; neat MOD 7
   PRINT nate MOD 11; aten MOD 11; ante MOD 11; neat MOD 11
   PRINT nate MOD 17; aten MOD 17; ante MOD 17; neat MOD 17
   PRINT
  END IF
  END IF
  END IF
END IF

   used(e) = 0
 END IF
NEXT
   used(t) = 0
 END IF
NEXT
   used(n) = 0
 END IF
NEXT
 used(a) = 0
NEXT

 


  Posted by Charlie on 2009-09-27 13:30:42
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