# 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 – Rand al'Thor Dec 29 '14 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. – Mr.Mindor Dec 30 '14 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. – Makyen Dec 30 '14 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. – Lopsy Dec 31 '14 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? – chasly - supports Monica Aug 16 '15 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
Right - Half height - hole to top edge.

• A hacksaw cannot cut a hole in the middle of a surface. – Sparr Dec 30 '14 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. – Aaron Dufour Dec 30 '14 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. – JonTheMon Dec 30 '14 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. – Makyen Dec 30 '14 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. – Aaron Dufour Dec 30 '14 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. – Florian F May 20 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. – Lopsy Dec 30 '14 at 2:30
• @Lopsy I fixed my answer, the new solution should be correct. Thanks for your feedback. – GOTO 0 Dec 30 '14 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. – Ceraus Dec 30 '14 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 – TehShrike Dec 30 '14 at 15:46
• @TehShrike Probably. Healing the cut is not required anyway. – GOTO 0 Dec 30 '14 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. – Rand al'Thor Dec 29 '14 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 Dec 29 '14 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. – supercat Dec 29 '14 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. – chasly - supports Monica Aug 16 '15 at 16:59

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 Dec 30 '14 at 22:53