[bonanova]

I find these to be fun.

This is similar to a previous one, but the chain is now longer.

A gold chain of 119 links is to be used as currency.

That is, at any given time an arbitrary number of links - from 1 to 119 - must be available to close a transaction.

What is the minimum number of links you would need to cut, now, to accomplish this?

[Guest]

I find these to be fun.

This is similar to a previous one, but the chain is now longer.

A gold chain of 119 links is to be used as currency.

That is, at any given time an arbitrary number of links - from 1 to 119 - must be available to close a transaction.

What is the minimum number of links you would need to cut, now, to accomplish this?

Eh... I missed the previous one, so

7 links?

1, 2, 4, 8, 16, 32 and 56?

[Guest]

I found the smallest cut count as 4. :

4+1+8+1+16+1+32+1+63 = 119

( oooo c oooooooo c oooo ....)

But I don't think that this is the smallest cut count. Because up to 159 pieces can be obtained by 4 cuts:

5+1+10+1+20+1+40+1+80 = 159

So the solution for 119 maybe 3, but can't consider such a case??

[Guest]

I found the smallest cut count as 4. :

4+1+8+1+16+1+32+1+63 = 119

( oooo c oooooooo c oooo ....)

But I don't think that this is the smallest cut count. Because up to 159 pieces can be obtained by 4 cuts:

5+1+10+1+20+1+40+1+80 = 159

So the solution for 119 maybe 3, but can't consider such a case??

I see where my misunderstanding is now. Thanks nobody.

[Guest]

I found the smallest cut count as 4. :

4+1+8+1+16+1+32+1+63 = 119

( oooo c oooooooo c oooo ....)

But I don't think that this is the smallest cut count. Because up to 159 pieces can be obtained by 4 cuts:

5+1+10+1+20+1+40+1+80 = 159

So the solution for 119 maybe 3, but can't consider such a case??

4 cuts,

4 + 1 + 8 + 1 + 16 + 1 + 32 + 1 + 55 = 119

3 cuts could only give you 1 link resolution up to 63 links

4 + 1 + 8 + 1 + 16 + 1 +32

Unless we are missing something?

[Jiminy Cricket]

4 cuts,

4 + 1 + 8 + 1 + 16 + 1 + 32 + 1 + 55 = 119

3 cuts could only give you 1 link resolution up to 63 links

4 + 1 + 8 + 1 + 16 + 1 +32

Unless we are missing something?

I think you're missing the fact that you have 55 links all together.

You have cuts that go to 63, right?

If you wanted 64 you take 55+8+1, etc...

[Prof. Templeton]

I see where my misunderstanding is now. Thanks nobody.

I had the same misunderstanding, but now I see that when you cut a link, you unbend it and disconnect it from the chain and rebend it back, so you end up with three pieces. The two smaller chains and the cut link. If you had a 5 link chain and cut it once, you could get two 2 link chains and 1 link.