Problem 056
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Problem 056
The problem isn't quite clear, where it says 'a,b<100'
for those who don't really know math notation(like me), it could mean either a<100 and b<100 or a<b<100
anyone else run into that problem?
for those who don't really know math notation(like me), it could mean either a<100 and b<100 or a<b<100
anyone else run into that problem?
Re: 056  Digital Sum
It's shortform for a<100 & b<100.
Re: 056  Digital Sum
I think most people know that "," ist just an "and". Its obvious.
Re: 056  Digital Sum
Obviously, (s)he didn't know that.

 Posts: 3
 Joined: Sat Feb 04, 2012 8:44 am
Re: Problem 056
Hi,
I have a question about this problem.
I guess there's a way to find the solution without doing the full calculations. If I am right, it's possible to have a hint ?
Thanks.
I have a question about this problem.
I guess there's a way to find the solution without doing the full calculations. If I am right, it's possible to have a hint ?
Thanks.
Re: Problem 056
No, I think you have to do all of the calculations. It's not too many, since the maximum exponent is 99.germanparente wrote: I guess there's a way to find the solution without doing the full calculations. If I am right, it's possible to have a hint ?
To solve this problem, you must learn how to accurately multiply integers which are too big to fit in standard 32 or 64bit variables and find the digits of the result.
Re: Problem 056
I am fairly confident in my algorithm, but am not getting the correct answer. Could someone knock the dust off of their old solution and maybe provide a few digital sums for large values of a and b for me to check my results against?
Thanks!
Thanks!
Re: Problem 056
digitSum(20^{14}) = 22petersc wrote:Could someone knock the dust off of their old solution and maybe provide a few digital sums for large values of a and b for me to check my results against?
digitSum(45^{67}) = 450
digitSum(94^{37}) = 310
Re: Problem 056
Here are some digit sums for a=4:
4^1 : 4
4^2 : 7
4^3 : 10
4^4 : 13
4^5 : 7
4^6 : 19
4^7 : 22
4^8 : 25
4^9 : 19
4^10 : 31
4^20 : 61
4^30 : 82
4^40 : 112
4^50 : 115
4^60 : 172
4^70 : 202
4^80 : 205
4^90 : 244
4^99 : 262
4^1 : 4
4^2 : 7
4^3 : 10
4^4 : 13
4^5 : 7
4^6 : 19
4^7 : 22
4^8 : 25
4^9 : 19
4^10 : 31
4^20 : 61
4^30 : 82
4^40 : 112
4^50 : 115
4^60 : 172
4^70 : 202
4^80 : 205
4^90 : 244
4^99 : 262
_{Jaap's Puzzle Page}
Re: Problem 056
Thank you both for your prompt responses.
Powers of 4: CHECK!
20^14: 22
But... alas...
45^67: 540 (Strangely a transposition of the same digits in Thundre's answer)
94^37: 350
I guess I've got some digging to do.
Thanks again.
Powers of 4: CHECK!
20^14: 22
But... alas...
45^67: 540 (Strangely a transposition of the same digits in Thundre's answer)
94^37: 350
I guess I've got some digging to do.
Thanks again.

 Posts: 2
 Joined: Fri Jun 26, 2015 11:56 am
Re: Problem 056
Do natural numbers include number zero as well? I googled the definition of natural numbers and this is what I found:
noun
the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.
noun
the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.
Re: Problem 056
Do you think including or excluding zero will make a difference to the answer of the problem?Archangelix wrote:Do natural numbers include number zero as well? I googled the definition of natural numbers and this is what I found:
noun
the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.
_{Jaap's Puzzle Page}

 Posts: 2
 Joined: Fri Jun 26, 2015 11:56 am
Re: Problem 056
Hmmm... sorry, nvm. I misunderstood the problem. Now that I see the discussions in this forum I understand what's actually being questioned here.jaap wrote:Do you think including or excluding zero will make a difference to the answer of the problem?Archangelix wrote:Do natural numbers include number zero as well? I googled the definition of natural numbers and this is what I found:
noun
the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.