# Dissection Puzzle - The Umbrella Stand

You own a square-shaped table. You want to drill a small hole in the center to place an umbrella stand. Unfortunately, you're a little drunk:

Alas. Fortunately, not all is lost. You are sober now, and have a hacksaw.

(a) Cut the table into two pieces. Reassemble them to make a square-shaped table the same size as the original, but with the circular hole in the exact center. The cut does not have to be a straight line, but it must divide the table into exactly two pieces.

(b) Now, minimize the length of the cut.

In this puzzle, everything is 2D. No tricky 3D cuts. Note added in later, after people started rightly questioning what a hacksaw can do: Don't worry about what cuts are physically possible with a hacksaw. Any division of the table into two pieces is allowed.

WARNING: When I give this puzzle to people, about 10% of them see the solution right away, about 30% figure out part (a) quickly and then spend varying amounts of time on part (b), and the other 60% give up. If you scroll down and look at the comments or answers, you will have robbed yourself of a deep 'aha!' moment.

• I think this is quite easy, but can't be bothered to make an image file demonstrating the answer. Let someone else have the rep :-p Commented Dec 29, 2014 at 15:43
• IMO the hole is already in a fine place, just turn the table so the hole is on the side of the sun. Too often I am sitting at a table with an umbrella and half the table or seats are still in the sun. An offset center would resolve that. Commented Dec 30, 2014 at 16:00
• Given that there are two solutions in the answer you have accepted, it is unclear which solution you consider correct. It is also unclear if you are actually intending to apply the full real-world constraint of having only a hacksaw to perform the cutting. In addition, a couple of solutions assume that there is the ability to fill gaps left by the hacksaw cut. You might want to clarify if this is permitted. Commented Dec 30, 2014 at 23:08
• @Mayken I consider JonTheMon's solution the canonical one. I should have been more careful about saying "hacksaw"; I've added a note to the question. The answers proposing hacksaw-specific cuts can stay, and I've upvoted some of them for ingenuity. Thanks for telling me to clarify the original puzzle. Commented Dec 31, 2014 at 0:09
• There are too many ways to do this. Can we make it more interesting by restricting it to only straight cuts and no drilling allowed? Commented Aug 16, 2015 at 17:03

Depending on your saw and skill, cut the hole in the middle where you want it, and use that piece to plug your mistake hole.

Originally I was going to suggest you cut an L shaped piece off the left and bottom and put it on the top and right. You would cut off:
Left - Half width - hole to right edge
Bottom - Half height - hole to top edge.

• A hacksaw cannot cut a hole in the middle of a surface. Commented Dec 30, 2014 at 2:41
• So, which of these is considered the correct answer? The first ignores the physical reality of a hacksaw, while the last only wins over other posted answers if you assume the hacksaw is larger than the hole (I have one that would fit, so I don't think that's a valid assumption). Although the winner depends to some degree on the ratios of the size of the table, size of the hole, and amount of displacement. Commented Dec 30, 2014 at 17:47
• @AaronDufour I think the first answer is what he was going for. The type of saw (hack, laser, band, whatever) would limit the type of cuts you could do. If you weren't limited, the first. If you were really limited (e.g. band saw), the second one would be more likely. If you had something like a jig saw, GOTO's answer would be the best. Commented Dec 30, 2014 at 21:15
• @AaronDufour, Given that a hacksaw removes some material (sawdust) and can not cut a hole in the middle of a surface, only the second method here (of all currently posted) provides a solution that does not leave a hole (e.g. a cut-line of removed material) in the table and can be performed (reasonably) with a hacksaw. While it might be possible to fill the gaps of some of the cuts suggested, that is not provided for in the question. The second method here has edges that have been joined, but not gaps. Commented Dec 30, 2014 at 23:02
• @Makyen The question says "Reassemble them to make a square-shaped table the same size as the original" which isn't possible even in the second solution here if we admit that the hacksaw removes material. So I don't think that's a good argument for or against any of the answers. Commented Dec 30, 2014 at 23:43

JonTheMon and xnor's solutions assume we have superior equipment and skill, but the question states that we "have a hacksaw". Well with a hacksaw, we must start from an exposed side; we can't start a cut in the middle of a plank!

The most efficient "side" would be the current hole:

If the hacksaw won't fit in the hole, we "cut an L shaped piece off the left and bottom", as stated first by JonTheMon.

Edit: I yield! GOTO0 found an even shorter practical solution.

• Unlike the intended solution this solution works without moving a leg to a silly place. Commented May 20, 2021 at 8:31

As pointed out in a previous answer, cutting a hole in the middle of the table may be unfeasible if everything you have is a hacksaw. Using the existing hole as a starting point, the cut can be reduced to the length of a single segment bifurcating on both end to meet the old and the newly cut hole tangentially at a convenient distance. Something like this.

Then swap the two fragments of the table.

## Update

The solution above divides the table in three pieces, which is not ok according to the problem statement. Here's another solution that produces only two pieces.

Update 2 - Credits to Ceraus for seeing this: Depending on your ability to cut sharp curves with the saw, this solution can be further optimized by starting the cut as close as possible to the line that joins the centers of both circles.

• Doesn't this cut the table into three pieces? Though I guess you could patch that by having a single line running from the hole to a circle cut in the center. Commented Dec 30, 2014 at 2:30
• @Lopsy I fixed my answer, the new solution should be correct. Thanks for your feedback. Commented Dec 30, 2014 at 2:54
• Can't believe I didn't see that! Although... you could make the cut slightly shorter by starting it as close as possible to the center of the table, then swerve before the center as in your first version. Commented Dec 30, 2014 at 2:59
• I wouldn't actually want to use this solution - it would be nearly impossible to heal the line cut through the board, even though the hole would be in the correct place Commented Dec 30, 2014 at 15:46
• @TehShrike Probably. Healing the cut is not required anyway. Commented Dec 30, 2014 at 15:54

You cut a square like this:

And rotate it 180 degrees.

The cut square (or rectangle) simply needs to have its centerpoint be halfway between the hole and the center of the square, and to be large enough to contain the hole.

Boy do I feel silly seeing the intended solution...

• +1 for effort! Making images was just what I couldn't be a***d to do. Commented Dec 29, 2014 at 16:09
• @randal'thor The images weren't actually hard to make. I just drew a square, cropped it, rotated it, and copied it back.
– xnor
Commented Dec 29, 2014 at 16:14
• Your solution would work if the requirement was that the table be divided using a combination of straight cuts; the cut length could be minimized by using a tilted rectangle which is just a teensy bit larger than a rectangle that circumscribes the accidental and proper locations of the hole. Commented Dec 29, 2014 at 18:13
• You can't do that with a hacksaw because you can't start the cut. You would have to drill first and that would create another problem hole. Commented Aug 16, 2015 at 16:59

I don't know why nobody came up with this answer.

Of course, you would have one leg sticking up in the air, but nowhere does it say it can't. In other solutions the leg is moved away from the corner, it didn't seem to be a problem either. So, ...

• Hindsight is 20/20, but if "hacksaw" was replaced with "laser saw with an infinitesimally narrow cut", and "table" was replaced with "tabletop", most of this question's confusion would have been erased.
– JLee
Commented Feb 25 at 11:29

As long as people are getting into impossible cuts with a hacksaw, I'm surprised no one has offered this solution...

Obviously, it can't be done, maybe with patience with a jigsaw. Also, hole saws exist.

Just me being pedantic, or the opposite, whichever.

• That's the already-accepted answer, although it's not totally realistic for the kind of cut that's possible with only a hacksaw.
– A E
Commented Dec 30, 2014 at 22:53