Math Is Fun Forum

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Simple, but...

There are 3 flies on a sqare table with side 1.
You have circle flapper with diameter 1.
Can you be sure that you can kill at least 2 flies with 1 hit? (if you are very presice, and assuming the flies are slightingly small)
And Why?

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IPBLE:  Increasing Performance By Lowering Expectations.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Simple, but...

I suppose either you are sure to kill all of them or you ain't sure of anything.

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X'(y-Xβ)=0

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Simple, but...

You can be sure of killing 1 unless your aim is terrible.

If the flies were at three corners you could get 2 by aiming midway along one side.

So ... if you were the flies how could you do better?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Simple, but...

I think it's time for a badly drawn diagram!

---------------------------
|     X                         |
|                                |
|                                |
|                                |
|                                |
|                              X|
|                                |
| X                             |
----------------------------

So, one fly goes in the corner, and the other two flies go near to, but not at, the corners adjacent to the first corner. I'm fairly certain that you can only hit one of these.

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It wanted to be normal.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Simple, but...

Great graph!
I actually begin to think this way- Is it possible to make all 3 distances between the 3 flies larger than 1? If there is such a chance, then no guarantee to kill 2 of the flies.
I think the graph above does represent one of this situation if the distances are equal.

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X'(y-Xβ)=0

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Simple, but...

lets see:

bottom left of square (0,0) to top right (1,1), let distance from left edge for top (and then also distance from bottom edge to the right fly along respective axis) be denoted by a:

(0,0), (a,1), (1,a)

this value will be the value given the maximum distance between all 3 points:

this distance is

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The End Of All Things To Come.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Simple, but...

A(0,0)B(0,1)C(1,1)D(1,0)

Flies' positions:
(0,0) (1,0.2) (0.2,1)
Distances:
√(1.04), √(1.28), √(1.04) ---------all larger than 1, so you cannot kill two of them at the same time

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X'(y-Xβ)=0