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Hill Numbers Settlement (Posted on 2010-07-15) Difficulty: 2 of 5
A 5-digit base ten positive integer of the form ABCDE is called a hill number if the digits B and D are each equal to the sum of the digits to their immediate left and right, that is, B = A + C and D = C + E. (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 hill number, given that x is a base ten positive integer chosen at random between 10000 and 99999 inclusively.

No Solution Yet Submitted by K Sengupta    
Rating: 1.6667 (3 votes)

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Climbing, climbing (solution) | Comment 1 of 4
There are 330 five-digit numbers between 10000 and 99999 which meet the definition, so the probability is 330/90000 or .0036666...
  Posted by ed bottemiller on 2010-07-15 13:58:28
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