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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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Some Thoughts possible solution | Comment 1 of 5
Either I am wrong or this is D1.

Whatever A+C (mod 10) is, there is a 1/10 chance that B is equal to it.  Likewise for D and F.

If the digits were independent the solution would be (1/10)(1/10)(1/10) = 1/1000. 

The problem is A cannot be 0.  I am worried this may cause a ripple effect because now C cannot equal B.

I am pretty sure this doesnt matter since D still has a 1/10 chance even if there is a limitation on C.

So I am going with 1/1000


  Posted by Jer on 2011-03-09 14:58:17
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