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
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