Ramathdom Noos
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How about logic problems that use elegant maths instead of problems of the form "Let's try every different permutation and mathematical combination of these letters and numers till we find something that might be right" Let me throw one out (this is an oldie so is probably know by some here) Take a look at the diagram here. It shows a flat area of land surrounded by a moat which is surrounded by flat land at the same level as the inside piece of land. The moat is 1 unit wide and filled with crocodiles. 2 parts: 1. Given 2 boards 0.9 of a unit long, how can you create a bridge to cross the moat. No ties, no tools, no nothing. Just two boards. 2. Is it possible to create a bridge using boards 0.5 units long? If so, how many boards are needed? Assume: o The boards are only wide enough to walk along. o They are sufficiently strong to hold whatever weight is needed o They are non-slip boards o They are a light brown colour o The crocs are hungry cheers, Chris Maunder
1. The moat is .5 units wide. .... (Outside - Flat area) / 2 so 2 .9 unit boards can be used easily with one on each side. 2. considering in the real number plane that boards of .5 units would not be engineering style sound. A .5 unit board could be placed diagonal on any corner of the outside and another used to connect across to the morner of the flat area. So 4 boards could be used. Or you could just walk around the outside. Regardz Colin J Davies
Sonork ID 100.9197:Colin
You are the intrepid one, always willing to leap into the fray! A serious character flaw, I might add, but entertaining. Said byRoger Wright about me.
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1. The moat is .5 units wide. .... (Outside - Flat area) / 2 so 2 .9 unit boards can be used easily with one on each side. 2. considering in the real number plane that boards of .5 units would not be engineering style sound. A .5 unit board could be placed diagonal on any corner of the outside and another used to connect across to the morner of the flat area. So 4 boards could be used. Or you could just walk around the outside. Regardz Colin J Davies
Sonork ID 100.9197:Colin
You are the intrepid one, always willing to leap into the fray! A serious character flaw, I might add, but entertaining. Said byRoger Wright about me.
I screwed up. See the updated image. Everythings square. Moat is 1 unit wide. Need sleeeeep.... cheers, Chris Maunder
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How about logic problems that use elegant maths instead of problems of the form "Let's try every different permutation and mathematical combination of these letters and numers till we find something that might be right" Let me throw one out (this is an oldie so is probably know by some here) Take a look at the diagram here. It shows a flat area of land surrounded by a moat which is surrounded by flat land at the same level as the inside piece of land. The moat is 1 unit wide and filled with crocodiles. 2 parts: 1. Given 2 boards 0.9 of a unit long, how can you create a bridge to cross the moat. No ties, no tools, no nothing. Just two boards. 2. Is it possible to create a bridge using boards 0.5 units long? If so, how many boards are needed? Assume: o The boards are only wide enough to walk along. o They are sufficiently strong to hold whatever weight is needed o They are non-slip boards o They are a light brown colour o The crocs are hungry cheers, Chris Maunder
Chris Maunder wrote: 1. Given 2 boards 0.9 of a unit long, how can you create a bridge to cross the moat. No ties, no tools, no nothing. Just two boards. Depending on how thick the boards were you could angle them so that the moat formed the bottom of a triangle /\ (thickness matters only so that they can support enough weight without falling past each other) Chris Maunder wrote: 2. Is it possible to create a bridge using boards 0.5 units long? If so, how many boards are needed? I'm not seeing it as being possible, but it probably is and I'm just not thinking right ;) James "Java is free - and worth every penny." - Christian Graus
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Chris Maunder wrote: 1. Given 2 boards 0.9 of a unit long, how can you create a bridge to cross the moat. No ties, no tools, no nothing. Just two boards. Depending on how thick the boards were you could angle them so that the moat formed the bottom of a triangle /\ (thickness matters only so that they can support enough weight without falling past each other) Chris Maunder wrote: 2. Is it possible to create a bridge using boards 0.5 units long? If so, how many boards are needed? I'm not seeing it as being possible, but it probably is and I'm just not thinking right ;) James "Java is free - and worth every penny." - Christian Graus
James T. Johnson wrote: I'm not seeing it as being possible, If not, why not? cheers, Chris Maunder
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James T. Johnson wrote: I'm not seeing it as being possible, If not, why not? cheers, Chris Maunder
Chris Maunder wrote: If not, why not? The bridge idea won't work because you couldn't get 1 unit of distance out of it (the sum of 2 sides is always greater than the third side; 0.5 + 0.5 = 1 so we know that the distance spanned will always be less than 1 unit. AH! If you have two wooden boards end to end, and hold them in the water; they should swell a little, thus making them slightly larger than 1 unit when end to end; the pressure resulting from fitting them in between the moat walls might hold the boards. The same principle used in old boats and kegs to make them water tight. James "Java is free - and worth every penny." - Christian Graus
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How about logic problems that use elegant maths instead of problems of the form "Let's try every different permutation and mathematical combination of these letters and numers till we find something that might be right" Let me throw one out (this is an oldie so is probably know by some here) Take a look at the diagram here. It shows a flat area of land surrounded by a moat which is surrounded by flat land at the same level as the inside piece of land. The moat is 1 unit wide and filled with crocodiles. 2 parts: 1. Given 2 boards 0.9 of a unit long, how can you create a bridge to cross the moat. No ties, no tools, no nothing. Just two boards. 2. Is it possible to create a bridge using boards 0.5 units long? If so, how many boards are needed? Assume: o The boards are only wide enough to walk along. o They are sufficiently strong to hold whatever weight is needed o They are non-slip boards o They are a light brown colour o The crocs are hungry cheers, Chris Maunder
How deep is the moat? Put one end of a board into the water a little over half way, with the other end on land. Walk down the non-slip board with the other board in hand and place one end on the board you are standing on and the other end on the opposite bank. For .5 unit boards, use 3 like this: \-/. The middle board would rest on the other 2, just out of the crocs' reach.
Jason Henderson
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"Like it or not, I'm right!" -
How deep is the moat? Put one end of a board into the water a little over half way, with the other end on land. Walk down the non-slip board with the other board in hand and place one end on the board you are standing on and the other end on the opposite bank. For .5 unit boards, use 3 like this: \-/. The middle board would rest on the other 2, just out of the crocs' reach.
Jason Henderson
quasi-homepage
articles
"Like it or not, I'm right!"Impressive solution !! Regardz Colin J Davies
Sonork ID 100.9197:Colin
You are the intrepid one, always willing to leap into the fray! A serious character flaw, I might add, but entertaining. Said byRoger Wright about me.
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Impressive solution !! Regardz Colin J Davies
Sonork ID 100.9197:Colin
You are the intrepid one, always willing to leap into the fray! A serious character flaw, I might add, but entertaining. Said byRoger Wright about me.
Thanks, I wonder if its right. What am I saying?? Of course it is.
Jason Henderson
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articles
"Like it or not, I'm right!" -
How deep is the moat? Put one end of a board into the water a little over half way, with the other end on land. Walk down the non-slip board with the other board in hand and place one end on the board you are standing on and the other end on the opposite bank. For .5 unit boards, use 3 like this: \-/. The middle board would rest on the other 2, just out of the crocs' reach.
Jason Henderson
quasi-homepage
articles
"Like it or not, I'm right!"What's holding the board down? You step along the board and it will tip over into the moat. As for using 3 boards, how do you get the 3rd board on the other side of the moat, and how do you ensure it's secured so it doesn't flip over when you put weight on it? cheers, Chris Maunder
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What's holding the board down? You step along the board and it will tip over into the moat. As for using 3 boards, how do you get the 3rd board on the other side of the moat, and how do you ensure it's secured so it doesn't flip over when you put weight on it? cheers, Chris Maunder
put the boards like this:
--\-----+
\ |
X |
/ \ |
/ \ |
-+ \|
+-- Andrew.
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What's holding the board down? You step along the board and it will tip over into the moat. As for using 3 boards, how do you get the 3rd board on the other side of the moat, and how do you ensure it's secured so it doesn't flip over when you put weight on it? cheers, Chris Maunder
Chris Maunder wrote: What's holding the board down? You said it was non-slip. :-D If they are non-slip you could easily walk down one without falling in plus, it should be able to hold the other board in place. Here are graphic illustrations: Scenario 1:
|++ ===|
| ++ === |
| ++ === |
|++
| ++ |Scenario 2:
|\ /|
| \ / |
| \-----/ |
|~\ /~|
| \ / |Jason Henderson
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"Like it or not, I'm right!" -
put the boards like this:
--\-----+
\ |
X |
/ \ |
/ \ |
-+ \|
+-- Andrew.
Good answer! What about the .5 length boards?
Jason Henderson
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articles
"Like it or not, I'm right!" -
Chris Maunder wrote: What's holding the board down? You said it was non-slip. :-D If they are non-slip you could easily walk down one without falling in plus, it should be able to hold the other board in place. Here are graphic illustrations: Scenario 1:
|++ ===|
| ++ === |
| ++ === |
|++
| ++ |Scenario 2:
|\ /|
| \ / |
| \-----/ |
|~\ /~|
| \ / |Jason Henderson
quasi-homepage
articles
"Like it or not, I'm right!"Ah - I getcha. The moat is 1 unit deep. cheers, Chris Maunder
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Good answer! What about the .5 length boards?
Jason Henderson
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"Like it or not, I'm right!"couldn't work 'cause hypotenuse (sp?) is biggest side, minimum board length with this setup would be sqrt(2)/2? [edit] that's wrong minimum board length, can't be bothered to work the proper one out :-D got packing to do... [/edit] -- Andrew.
