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Tricky Ten Digit Number (Posted on 2006-07-31) Difficulty: 3 of 5
Find a number ABCDEFGHIJ, with all its digits different, such that:
  • A, C, E, G, and I are odd
  • HIJ is a multiple of BCD
  • GH is a multiple of AB
  • HIJ/BCD equals GH/AB

No Solution Yet Submitted by Yosippavar    
Rating: 4.2500 (4 votes)

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Solution | Comment 7 of 10 |

If GH/AB = HIJ/BCD = 2

Then A & C would be 1,3,5,7 and G & I would be 3,5,7,9

B & D would be 6,8 & J & H would be 2,6 Which is not possible

If GH/AB = HIJ/BCD = 3

Then A = 1,3 & G = 3,9 but B has to be 2 hence H has to be 6.

D has to be 8 & J has to be 4 and as regards C & I following possibilities exist

a) If C is 1 then I = 5

b) If C is 3 then I = 1

c) If C is 5 then I = 7

d) If C is 7 then I = 3

e) If C is 9 then I = 9

Possibilities b), d) & e) are not possible. And possibility c) will make H odd hence possibility a) would be true.

Then A has to be 3 & G has to be 9

the remaining odd & even numbers E=7, F=0

So ABCDEFGHIJ is 3218709654

Have not tried possibility of 4 but that may not be possible.

 

 

 

 

 


  Posted by CMAS23 on 2006-08-09 01:08:48
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