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        riddles >> hard >> Digital Transference Problem Revisited
        
(Message started by: K Sengupta on Nov 28^th, 2005, 12:29am)

Title: Digital Transference Problem Revisited
Post by K Sengupta on Nov 28^th, 2005, 12:29am

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.

Title: Re: Digital Transference Problem Revisited
Post by Grimbal on Nov 28^th, 2005, 2:38am

:( I don't even understand the question. What are you doing to N? Can you give an example?

Title: Re: Digital Transference Problem Revisited
Post by K Sengupta on Nov 30^th, 2005, 11:59pm

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).