## Thursday, January 14, 2010

### Help Cutting the Fire Log

You can buy a fire log. It costs 10 cents to cut the log into two parts. What is the least expensive way to cut this log into 10 equal parts? How much do you need to pay? What is the most expensive?

Enter your answer on our Family Puzzle Marathon page. Solve three and get a prize!

W said...

Least expensive:

One slice down the middle to separate the log into two separate parts. Keeping the log intact (even though its split down the middle), use 4 cuts to cut perpendicular to the middle.

Not sure if this is possible to do but I would even cut the log width-wise in the middle then stack the logs together along another cut line and cut the huge stack with one cut.

(Cut along the dotted line)
___________________________
| |
|---------------------------|
| |
|___________________________|

and then 4 cuts down perpendicular to the middle cut (to make 5 parts on each part of the log now) but make a cut and then stack the logs so that you can use one cut to separate two different logs into 4 parts.

For instance:

Cut here:

*
|----|-----|-----|-----|-----|
| | | | | |
|----|-----|-----|-----|-----|
*
|----|-----|-----|
| | | |
|----|-----|-----|
*

and by stacking, you cut along the starred line across two logs.

So if this is possible:

1 cut to separate into two logs: 10 cents
1 cut to separate the two logs into 4 pieces: 20 cents.
1 cut to separate the 4 pieces into 8 pieces:
30 cents.
1 last cut to separate 2 pieces into 4 pieces making 10 all together: 40 cents.

Hopefully all of that makes sense!

W said...

Oops, the spacing didn't work so the stacking isn't super clear!

Maria said...

I think I get your idea of stacking cut logs together and cutting them jointly to "fool" the wood seller that it is still one cut. And in fact, it may very well be, with these large automatic saws. Very creative!

But if you start stacking them together, I think you can get away with 3 cuts only! Who knows how? Feel free to either post description below or email me the answer drawing or sketch.

Maria said...

I was thinking why no one is answering this simple question.... till I realized that I made a mistake and mislead you all. Please never hesitate to tell me when I am wrong and something is impossible.

I am pretty sure now you can't do it with 3 cuts. W. is right - 4 cuts is the minimum.
Here is my attempt to draw what he or she described above.
Click to see the image

The maximum number of cuts is 9 = 90 cents.

Maria said...

Alin emailed me this solution at 2.51pm on january 15th:
click to open Alin's log cutting diagram
He assumed that we can't stack cut pieces on top of each other and beautifully showed how in this case we can manage with a min of 5 and max of 9 cuts. I think he also deserves a puzzle point (along with W.).

New puzzle tomorrow!

Maria said...