Comments on: The Traversal Problem (3 dimensions)

By: Saksham

Saksham — Mon, 04 Oct 2010 12:54:48 +0000

Yupp

Hope to see other nice questions.

By: Micky

Micky — Sun, 03 Oct 2010 09:17:42 +0000

That’s the ticket. Nice work. Sorry for the insult!
Notice the binomial sequences:

2d solution: [1]HCF(0 at a time) + [2]HCF(1 at a time) – [1]HCF(2 at a time)
3d: solution: [1]HCF(0 at a time) + [3]HCF(1 at a time) – [3]HCF(2 at a time) + [1]HCF(3 at a time)

4d: [1]HCF(0 at a time) + [4]HCF(1 at a time) – [6]HCF(2 at a time) + [4]HCF(3 at a time) – [1]HCF(4 at a time)

and so on…

By: Saksham

Saksham — Sun, 03 Oct 2010 07:25:20 +0000

And similar extension for 4 dimensions -
x + y + z + a – (HCF taken 2 at a time) + (HCF taken 3 at a time) – (HCF taken 4 at a time)

By: Saksham

Saksham — Sun, 03 Oct 2010 07:18:11 +0000

Oh ya sorry 6, Haha don’t insult my mnetal maths by asking to check on excel .
Nice resemblance to principle of inclusion-exclusion, and you demonstrate the solution very nicely!

By: Micky

Micky — Sat, 02 Oct 2010 13:04:56 +0000

That’s the right answer – excellent work.
Check it again, it gives 6 not 7.
In excel, type =2+3+4-GCD(2,3)-GCD(2,4)-GCD(3,4)+GCD(2,3,4)
I’ve put the full solution up now
Micky

By: Saksham

Saksham — Sat, 02 Oct 2010 12:22:14 +0000

Going by the 2D problem, can this be extended as
l + b + h – hcf(l,b) – hcf(b,h) – hcf(h,l) + hcf(l,m,n) ?

though for 2x3x4 it gives 7

By: Rick

Rick — Sun, 26 Sep 2010 20:33:25 +0000

Man it’s driving me bonkers! Would love to hear how it works!

By: Rick

Rick — Fri, 24 Sep 2010 15:30:02 +0000

Ok, thanks! Hope to hear soon!

By: Micky

Micky — Tue, 21 Sep 2010 17:57:56 +0000

give me a few days! busy part of the school term! micky

By: Rick

Rick — Tue, 21 Sep 2010 15:40:47 +0000

What’s the full solution?