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K Sengupta
Senior Riddler     Gender: Posts: 371 Digital Transference Problem Revisited   « on: Nov 28th, 2005, 12:29am » Quote Modify

Considering a K digit integer N ( where the last digit  of N is non-zero) the number L is constituted by deleting the first P digits of N and shifting a permutation of these P digits ( the definition of the said permutation being inclusive of the original  first P Digits of N) to the end of N.
IF:
(i) L is divisible by N such that L is not equal to N,
determine the total number of pairs (G,N) where 2<=P<=6 ,8<=K<=15 and Max(L,N)<10^15

(ii) If, in addition, the sum of the digits in N is a perfect M-th power with M being a positive whole number grater than 1, determine the total number
of distinct Quadruplets ( P,K, L,N) where  2<=P<=6 ,8<=K<=15 and Max(L,N)<10^15.

(iii) Determine the minimum possible magnitude of
the pair (L,N) separately for  each pair (P,K) where
2<=P<=6 ,8<=K<=15 and Max(L,N)<10^15. IP Logged
Grimbal
wu::riddles Moderator
Uberpuzzler      Gender: Posts: 7517 Re: Digital Transference Problem Revisited   « Reply #1 on: Nov 28th, 2005, 2:38am » Quote Modify I don't even understand the question.  What are you doing to N? Can you give an example? IP Logged
K Sengupta
Senior Riddler     Gender: Posts: 371 Re: Digital Transference Problem Revisited   « Reply #2 on: Nov 30th, 2005, 11:59pm » Quote Modify

Suppose N=32456789and for example we consider the first  3 digits(P=3,K=8) ,i.e.,352. All possible permutation of 352(including itself) are
324,342,243,234,423,432 so that  this gives six  available values  of L  by which are  56789324, 56789342,56789243,56789234,56789423,56789432.
Clearly, all these six values of L  may or may not satisfy all the  three conditions.
In case of multiple L values for a single N corresponding to a given choice of (P,K) , satisfying conditions of the problem - for example if there are 3 values of L -La1,La2 and La3- say for a single N=Na,P=Pa and K=Ka then   we would have 3 distinct quadruplets for (N,P,K,L)  corresponding to N=Na,P=Pa and K=Ka given by (N,P,K,L)= (Na,Pa,Ka,La1),(Na,Pa,Ka,La2) and (Na,Pa,Ka,La3).
 « Last Edit: Dec 1st, 2005, 3:30pm by Icarus » IP Logged

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