Posted by **Chris** on Monday, May 7, 2012 at 8:07am.

Find a six-digit even number containing no zeros and no repeating digits in which the first digit is four more than the second digit, the third digit is one less than the sixth digit, and the fourth and fifth digits when read as a single number equal the product of the first and sixth digits.

- math -
**Steve**, Monday, May 7, 2012 at 10:23am
abcdef

a=b+4

c=f-1

de=af

Let's see what de can be, and what af could then be. Remember that a>=5, since b>=1

de: af

14: 72 b=3 c=1 no

15: 53 no, odd

16: 82 b=3 c=1 no

18: 92 b=5 c=1 no, or 63 b=2 c=1 no

21: 73 no, odd

24: 83 no, odd

27: 93 no, odd

28: 74 b=3 c=3 no

32: 84 b=4 no

36: 94 b=5 c=3 no

42: 67 no, odd; 76 b=3 c=5 YES

54: 69 no, odd; or 96 b=5 no

56: 78 b=3 c=7 no, or 87 b=4 c=6 no

63: 79 or 97 no, both odd

72: 89 no, odd; 98 b=5,c=7 no

So, we are left with 735426

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