Determine the maximum value of a (base ten) positive integer N (with non leading zeroes) such that each of the digits of N, with the exception of the first digit and the last digit, is less than the arithmetic mean of the two neighboring digits.

Note: Try to solve this problem analytically, although computer program/ spreadsheet solutions are welcome.

The largest (base 10) integer, with each digit, with the exception of the first and last digit, less than the arithmetic mean of its two neighboring digits is the 8-digit palindromic number 96433469.

Following is a list of all other 8-digit (base 10) positive integers that have the same arithmetic mean relationship among its neighboring digits
(Several other integers with this relationship with less digits also exist; the minimum being the 3-digit integer: 100):

95322359
95322358
95211259
95211249
95211248
95211247
95200259
95200149
95200148
95200139
95200138
95200137
95200136
94211259
94211249
94211248
94211247
94100259
94100149
94100148
94100139
94100138
94100137
94100136
93100259
93100149
93100148
93100139
93100138
93100137
93100136
85322359
85322358
84211259
84211249
84211248
84211247
84100259
84100149
84100148
84100139
84100138
84100137
84100136
83100259
83100149
83100148
83100139
83100138
83100137
83100136
74211259
74211249
74211248
74211247
73100259
73100149
73100148
73100139
73100138
73100137
73100136
63100259
63100149
63100148
63100139
63100138
63100137
63100136

Edited on September 28, 2008, 7:43 am

Posted by Dej Mar on 2008-09-27 22:12:41