A positive integer N fulfills the following demands:.
N is a 7 digit number.
N's digits can be arranged as seven distinct members of an arithmetic progression(either ascending or descending) .

N is a multiple of 11.

How many positive integers like N exist?
Evaluate the lowest and the highest N.
BONUS : How about 8 digits? Nine? All ten?
  Rem: It is D4 for fully explained and errorless P&P result,might be significantly lower for software solution.    

(In reply to re: for 10 digits ?????? by Ady TZIDON)

The number 285120 in my answer is the number of permutations of the ten digits that constitute a number that's divisible by 11, but don't have a leading zero. Obviously it's too many to list them, but here are a few:

3864720519
3864720915
3864721509
3864721905
3864750219
3864750912
3864751209
3864751902
3864790215
3864790512
3864791205
3864791502
3865021479
3865021974
3865027419
3865027914
3865041279
3865041972
3865047219
3865047912
3865091274
3865091472
3865097214
3865097412
3865120479
3865120974
3865127409
3865127904
3865140279
3865140972
3865147209
3865147902
3865190274
3865190472
3865197204
3865197402
3865720419
3865720914
3865721409
3865721904
3865740219
3865740912
3865741209
3865741902
3865790214
3865790412
3865791204
3865791402

I guess I neglected to list the lowest and highest; sorry about that. The highest is 9876524130 and the lowest is 1024375869.

Posted by Charlie on 2010-12-11 15:51:35