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Hill Numbers Settlement II (Posted on 2011-03-09) Difficulty: 3 of 5
A 7-digit base ten positive integer of the form ABCDEFG is called a modified hill number if the digits B, D and F satisfies: B = A + C (mod 10) , D = C + E (mod 10) and F= E + G (mod 10) (Each of the capital letters in bold denotes a digit from 0 to 9, whether same or different.)

Determine the probability that x is a modified hill number, given that x is a base ten positive integer chosen at random between 1000000 and 9999999 inclusively.

No Solution Yet Submitted by K Sengupta    
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Solution solution | Comment 2 of 5 |

The numbers are determined by A, C, E and G, and any digits can be used in these four positions except that A cannot be zero in the range given.

There are 9 choices for A and 10 each for C, E and G, for a total of 9000 possibilities out of the 9999999 - 999999 = 9,000,000.

The probability is 9,000 / 9,000,000 = 1/1000.

Done this way it seems like a D2.

Another way of figuring it:

B has 1 chance in 10 of satisfying the condition, as does D, and the same for F. Multiplied together that's 1/1000.

Now it seems like a D1.

  Posted by Charlie on 2011-03-09 15:10:32
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