Cute Maths Problem I stumbled on in New Scientist today...

Stumbled onto this in a New Scientist today, and was stumped.. I cheated and read the answer, which I immediately regretted as it is such a very sensible solution..

Don't post answers if you figure it out, I will put it up later over the weekend. PM me if you feel the need to gloat, and I will list an "Honour Board" listing the order of correct answerers when I post the solution...

Can you solve this problem?

Two farmers inherit a square field containing a crop planted in a circle. Without knowing the exact size of the field or crop, or the crop’s position within the field, how can they draw a single line to divide both the crop and field equally?

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So the solution needs to work for all of the following variants:

Took a minute but it’s pretty simple.

The position of each circle within each square has a common feature.

Took me a little bit, but I figured it out. Your right, the solution is quite nice.

Just have the aliens who created the crop circles eat the farmers.

sooner.boomer said:

The position of each circle within each square has a common feature.

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Yes it does: the circle is INSIDE the square... [emoji12]

Zeus-cat said:

Just have the aliens who created the crop circles eat the farmers.

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There are two aliens. Each alien gets to eat one farmer each. But which half of the field and crop would each farmer be in? Where do the aliens look to make sure they each get one farmer?

You see what I did there?

I have a solution that works for all six drawings, but I don't think the six drawings represent the near-infinite number of cases possible. So my solution is probably wrong.

I came up with 2 different solutions, I'm sure neither of which are right.

Got it after 5 seconds......

My complaint is that the six pictures are not fully representative of the problem as stated. "Without knowing the exact size of the field or crop, or the crop’s position within the field,..." could also mean:

I think the solution that I have in mind will work for that case as well.

The solution is to forget about the crops and use the field to fly rockets.

Is the challenge to find a single line that will always work in any field, or a method to find the line that will work in a particular field but it would be different for the next field?

I'm pretty sure the latter is an easy solution but the former is impossible.

Nathan said:

The solution is to forget about the crops and use the field to fly rockets.

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I like the way you think.

Very clever puzzle.

snrkl said:

Yes it does: the circle is INSIDE the square... [emoji12]

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I think the solution would also work if the field was a circle and the crops were a square inside the circle.

BEC said:

I think the solution that I have in mind will work for that case as well.

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Likewise, I have a general solution. Physical task that two farmers can do with a string and one pole.

Bat-mite said:

My complaint is that the six pictures are not fully representative of the problem as stated. "Without knowing the exact size of the field or crop, or the crop’s position within the field,..." could also mean:

View attachment 343503

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Correct.

The diagrams are an aid, but you are correct, there is an infinite number of crop/field combinations.

snrkl said:

Correct.

The diagrams are an aid, but you are correct, there is an infinite number of crop/field combinations.

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The original diagrams are misleading because they all appear to have the center of the circle passing through the diagonal of the square. That is the "trivial solution", as the mathematicians say.

The general solution for the square (or rectangle) can be done by observation, some walking, a long string, and a pole. The general mathematical solution can be solved with ratios and relative distances without knowing absolute dimension.

And, as with most of these, a successful solution depends on already knowing the author's intent with "a single line".

dhbarr said:

And, as with most of these, a successful solution depends on already knowing the author's intent with "a single line".

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I think "a single line" is unambiguous. Don't have to make it complicated at all.

jsdemar said:

The general solution for the square (or rectangle) can be done by observation, some walking, a long string, and a pole. The general mathematical solution can be solved with ratios and relative distances without knowing absolute dimension.

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jsdemar said:

I think "a single line" is unambiguous. Don't have to make it complicated at all.

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The observation is a line, the walking is lines, the string is a line, the pole is a line

dhbarr said:

The observation is a line, the walking is lines, the string is a line, the pole is a line

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The observation is an action, the walking is an action that isn't necessarily on a straight line, the string is a line if taut with no obstructions, and the pole is a point on the x,y plane. :-]

sooner.boomer said:

The position of each circle within each square has a common feature.

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+1 ^

Nathan said:

The solution is to forget about the crops and use the field to fly rockets.

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+3 ^

sooner.boomer said:

The position of each circle within each square has a common feature.

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K'Tesh said:

+1 ^

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-1. There's a simple solution that doesn't depend on that illusion.

Okay, for cryin' out loud, what is it?!?

Mushtang said:

Is the challenge to find a single line that will always work in any field

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Correct - the solution will work with any field / crop combination...

Bat-mite said:

Okay, for cryin' out loud, what is it?!?

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Patience. I’ll post the answer later this afternoon my time.

[emoji12]