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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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Solution Solution Comment 4 of 4 |

There are 330 hill numbers inclusively between 10000 and 99999. The first and last being 11000 and 99099.
There are 90000 numbers inclusively between 10000 and 99999 (99999 - 10000 + 1 = 90000).
Therefore, the probability that a number chosen at random from the set of 90000 numbers is 330/90000 = 11/3000 = 0.00366.


  Posted by Dej Mar on 2010-07-15 18:35:26
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