Problem 45250. Be happy
check whether the given number is happy in bbase.
 A happy number can be defined as a number which will yield 1 when it is replaced by the sum of the square of its digits repeatedly. If this process results in an endless cycle of numbers containing 4, then the number is called an unhappy number.
This is the case for base10. For other bases, different scenerios would occur.
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Hi Asif: Can you give a little more detail to your solvers about what "happy" and "bbase' mean? Maybe link to Wikipedia reference pages?
https://en.wikipedia.org/wiki/Happy_number
Asif: If I am reading that reference correctly, then test suite problems 4 and 7 are incorrect. In fact, problem 4 has base b=4, and according to the reference b=4 is a "happy base" in which *all* numbers are happy.
thank u william for pointing that out.
i've modified the test suites.
kindly inform if u find any more discrepancies.
Asif: Yes, I am now seeing a discrepancy with problem 6, but all the others agree with my code.
william, so far i've understood the concept, test6 is correct.
https://en.wikipedia.org/wiki/Perfect_digital_invariant
have a look..I think it'll make things clear
but still if i'm wrong,do inform
Well, it appears to me that the number 742356 is a preperiodic point of the perfect digital invariant n=8 in base 3. However, since the perfect digital invariant is n=8 rather than n=1, this is not a happy number. At least, that is how I read it!
william
did u look into the nontrivial PDI portion?
i might have been wrongi 'll look into it when i get some time. i'm a bit busy now with my new job
Asif, Yes, I looked at the information on nontrivial perfect digital invariants. Near the end of that reference, there is a short section entitled "Relation to happy numbers" that indicates that in order for a number to be happy, it needs to be a perfect digital invariant with the value of 1. In this case, the invariant is 8 (or 22 in base3), so I interprete that as saying that it is a nontrivial PDI, but not happy.
william,
thanks man.. sorry i didn't go through all that info.
i've updated the problem.it should be okay now
Is test 10 wrong? n=3148 in base 13 cylces 79A079A0, not a happy number.
Jan Olsen is right and test 10 is definitely wrong. In iteration 5 most solvers (including Asif, it seems) translate dec2base(10,13) = ‘A’ to digital by ‘A’‘0’ = 17. The correct is of course 10, leading to the cycle noted by Jan. The test suite should be corrected.
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