Math Is Fun Forum
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#1 2015-08-07 04:01:20
- phanthanhtom
- Member
- Registered: 2012-06-22
- Posts: 290
Placing 4 counters on a 4x4 board
Original problem: 2015 IWYMIC team contest, problem 4:
"There is a 4×4 grid posted on the wall. Find the number of ways of placing two
identical red counters and two identical blue counters on four different squares of
the grid such that no column or row has two counters of the same color. "
The official answer is 3960. However, I could not reach this answer. Please help.
(The website of the competition is at imc-official.com, but it is seldomly updated).
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#2 2015-08-07 13:16:25
- ElainaVW
- Member
- Registered: 2013-04-29
- Posts: 580
Re: Placing 4 counters on a 4x4 board
Hello:
The official answer is correct.:)
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#3 2015-08-07 15:38:00
- phanthanhtom
- Member
- Registered: 2012-06-22
- Posts: 290
Re: Placing 4 counters on a 4x4 board
I trust that source, so I was just asking how can I reach that answer. Right now I can't even think of a way to get any answer.
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#4 2015-08-07 20:16:20
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Placing 4 counters on a 4x4 board
The official answer is correct.:)
Send me the nb file please.
I trust that source,
There is no trust in math, especially in combinatorics or probability where even the best get confused now and then.
Right now I can't even think of a way to get any answer.
Computation and PIE are two ways.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2015-08-08 16:45:32
Re: Placing 4 counters on a 4x4 board
There is confidence.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#6 2015-08-08 18:25:42
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Placing 4 counters on a 4x4 board
Not from me.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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