I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!

Friday, September 15, 2006

Government Subsidies

The government pays farmers a specific fee for each row of four trees that they plant. An enterprising, but dishonest farmer found a way of planting five rows of four trees using only ten trees. How did he do it?

Pne tree at each point in a pentagram with another tree at each line's intersection. Looking down each side of the five-sided star will have four trees in a row.

A little hill shaped like a half melon should do the trick. Plant one tree at the base of the hill on one side. Plant another due opposite. These two will be the endpoints of as many straight lines as you like. Four of them, with two more trees each, that gives us four rows with ten trees.

There are some very creative answers to this one. My answer was he planted the trees in the shape of a star. Draw a star and plant a tree at each intersection. You can see the five rows.

I'm not sure I buy the 10 trees in one line. I would think that produces one row?

Picture a basketball and put your finger on opposite sides (these are your first two trees). Then draw a straight line from end point to end point. Somewhere along that line, plant two trees.

Then rotate the ball a little bit, and draw a straight line in, planting two trees along that line.

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I am guessing he laid them out in a grid, but I don't know how he did it yet. I'll get back to you.

ReplyDeletePne tree at each point in a pentagram with another tree at each line's intersection. Looking down each side of the five-sided star will have four trees in a row.

ReplyDeleteSorry, that should read One tree at each point...

ReplyDeletePlanting all 10 in one straight line would produce 7 different rows of four trees.

ReplyDeleteA little hill shaped like a half melon should do the trick. Plant one tree at the base of the hill on one side. Plant another due opposite. These two will be the endpoints of as many straight lines as you like. Four of them, with two more trees each, that gives us four rows with ten trees.

ReplyDeleteThere are some very creative answers to this one. My answer was he planted the trees in the shape of a star. Draw a star and plant a tree at each intersection. You can see the five rows.

ReplyDeleteI'm not sure I buy the 10 trees in one line. I would think that produces one row?

I thought the half-melon theory was great!

Bravo to all the users who came up with the creative solutions. I got the star one immediately, but the others are quite creative.

ReplyDeleteActually, I still don't quite see how the half-melon idea works. Can someone explain in more detail?

ReplyDeleteThanks.

Picture a basketball and put your finger on opposite sides (these are your first two trees). Then draw a straight line from end point to end point. Somewhere along that line, plant two trees.

ReplyDeleteThen rotate the ball a little bit, and draw a straight line in, planting two trees along that line.

Then rotate the ball a little bit, ...

Hope that helps Andy

It helps. but of course those are not actually lines, they are curves.

ReplyDeleteI guess it all depends on how you define 'line' or in this case, row.

ReplyDeleteI agree the government inspector would have to pretty dumb to pay out on that type of trick, but ... ;-)