# How do you walk across a 10' x 10' hole using two 9' boards?

Given a 10' x 10' hole which is very deep, how do you walk across the hole using two boards that are each 9' long?

You can't jump, pole vault across, nail the boards together, or go around the hole.

You can start on any side you like, but once you start to cross, you must stay on the two boards. No stepping off on the sides.

• How wide is the hole? Commented May 29, 2015 at 15:30
• Also: "you can start on any side you like" -- in that case, I choose to start on the side that I'm trying to get to ;) Commented May 29, 2015 at 17:16
• In my mind for some reason there were walls either side. Gah! Commented May 30, 2015 at 1:27
• If we can't travel to the side of the hole, why can we support the boards there? It's a bizarre and arbitrary rule. Commented May 30, 2015 at 5:21
• Use the boards as stilts. With enough practice, the right speed and good timing you can stride (walk) across the hole without jumping or vaulting. Commented Jun 21, 2015 at 13:24

You put the first board

at a 45 degree angle across one corner

of the hole. Then you put the other one

with one end on the first board and the other end on the side of the hole.

Thanks to Julian Rosen and Geobits for their insight on how my drawing was bad. I updated it to be more accurate:

• How does that help you cross the hole with the two boards? It appears that your solution leaves them behind.
– Anon
Commented May 29, 2015 at 16:03
• @Anon I guess you should ask OP to clarify his question. When he use the word with, I guess he means using and not that you need to carry them along.
– A.D.
Commented May 29, 2015 at 16:06
• Cute diagram. But if I can't walk around the hole, how do I get the green board in place and how do I get onto the green board (which I think is about 5 feet away from the corner) to place the red board? The question isn't clear about what parts of the sides of the hole are accessible. Commented May 29, 2015 at 16:27
• If the hole is a square 10 feet on a side and the boards are 9 feet, then this won't quite reach. The distance from the center of the green board to the upper left corner is $10\sqrt{2}-9/2\approx9.64$. Commented May 29, 2015 at 16:34
• @JulianRosen Yea, the red board shouldn't go to the corner, but just straight vertical from some (among many) point along the green board. The diagram shows it wrong, but the text doesn't specify that it goes to the corner. Commented May 29, 2015 at 16:45

Here's a simple solution that lets you take both boards with you:

You're not allowed to walk around the hole, but clearly there must be some kind of a ledge on each side of the hole that you can use to support the end of a board on, even if it's too narrow to walk on. (Otherwise none of the answers work, and I'm fairly sure that the problem is unsolvable.) So just

place one board so that it reaches from the side you're on to one of the ledges, about halfway across. Pick up the second board and walk along the first to the ledge, then place the second board down so it reaches from the ledge to the other side. Step across to the second board (you can make the gap between the boards arbitrarily small, so this should not be a problem), pick up the first one and walk to the other side.

Ps. Note that this puzzle, as stated above, is a much simplified version of the classic moat-crossing problem. In the original problem, to which lorimer's answer would be a correct solution, the "hole" is actually an L-shaped corner in a moat, and you need to get from the outside to the inside corner of the L. This rules out "trivial" answers like mine and A.D.'s (but also prevents you from picking up both boards after you've crossed).

• Wouldn't this work with 1 board as well? Commented May 29, 2015 at 23:46
• @jpmc26: Only if the ledge is wide enough to stand on while you pick up the board and move it. Commented May 29, 2015 at 23:56
• That would also have to be the case to take both boards with you to the other side, though, as your answer suggests. ;) Commented May 30, 2015 at 0:00
• @jpmc26: Not really. With two boards, you can stand on one board while putting down / picking up the other. You never have to actually stand on the ledge. Commented May 30, 2015 at 0:02

Like this -- you put one board at an angle, then the other across.

• This is a good solution to the original problem, of which the puzzle asked above is a simplified / corrupted variant. +1. Commented May 30, 2015 at 18:24

Use one board to connect the south edge to the west-ward/east-ward edge. Use the second board and connect it to the first board to reach the end.