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| Author | Maths Problems |
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For Lord STB, post 38 is a nice story and a classic problem :D
Three uses are necessary and enough.
Denote all SoM by 1-12. First, compare 1,2,3,4 vs 5,6,7,8.
1. If equal, then the fake one is among the rest 4. Compare 1,2,3 vs 9,10,11.
1.1 If equal, then the fake one is 12. Compare 1 and 12 to see if 12 is heavier or lighter.
1.2 If 9,10,11 are heavier(lighter), then the fake one is heavier(lighter) and among 9,10,11. Compare 9 and 10 in the third step.
2. If not equal, let us say 1,2,3,4 are heavier WOLG. Compare 1,2,5,6 vs 3,7,9,10.
2.1 If equal, compare 1 and 4.
2.2 If 1,2,5,6 are heavier, then either 1/2 are heavier or 7 is lighter. Compare 1 and 2.
2.3 If 1,2,5,6 are lighter, then either 5/6 are lighter or 3 is heavier. Compare 5 and 6. | for SunnyDaisy:
gr8 buddy..gr8 way indeed..i was confused on how to see if fake is heavier or lighter
Compare 1 and 12 to see if 12 is heavier or lighter.
this step cleared my doubt..an easy step..but hard to catch | Start with 4 groups of 3 swords. Call them a, b, c and d.
Weigh a against b and weigh c against d. 2 measures. One will balance, one will not. The ones that balance you now know are the perfect swords. For simplicity, lets say a and b balance.
Measure a against c. If it balances, you know c are real and d are dodgy. If it doesn't balance, you know d are real and c are dodgy. For simplicity we'll say c is real. 3 measures at this point.
Measure 1 sword in group c against another sword in group c. If they balance, the left out sword is the dodgy one. 4 measure for a solution. IF they don't balance, 1 of those 2 is dodgy. measure against any of the many swords we already know are real (group a, etc). IT balances, it's legit and the other is dodgy, it doesn't balance, it's legit and the other is dodgy.
Another option. Obviously you'll place the swords on 1 at a time. When you place the 1st sword on, surreptitiously look at the weight. If the next sword is the same weight, you now know the weight of correct swords. Keep piling on, doing the maths in your head until the extra weight from the sword being piled on is ot the same. That will be the bad sword. If sword 1 and 2 are not the same weight, it will take a second measure to measure one of those against any other sword. It balances, it's the good one, the other is bad, it doesn't balance, it's the bad one, the other is good. | For 63, B-F:
The first part looks very good, but you did not reach all the way. Please try again.
You may not look at the scale when adding swords. That counts as multiple measurements. | The triangles.
It is easy to make one equilateral triangle with 3 matches. To make 2 equilateral triangles, you only need 5 matches because you can reuse one match for the second triangle.
How many matches do you need to make at least 6 equilateral triangles? | for Lord STB:
11? | How many matches do you need to make at least 6 equilateral triangles?
I need 6 matches ;) | | I prefer toothpicks. However, with six toothpicks you can make 8 equilateral triangles. | | That seemed easy. Lets make 7 equilateral triangles of the same size. You may not have other triangles of different size in your solution. How many matches/toothpicks/metal beams/lines do you need? | Lets make 7 equilateral triangles of the same size.
I need 9 | | I need 9 and duct tape ^^ | for Sven91:
lol with metal beams I don't need any duct tape :P | One of the most famous classic problems -
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? | for Lord harddude:
yes | | ^Explaination? | You should stick to it. Because if you pick one door and stick to it you have 1/3 of getting the car. That means you have 2/3 of getting a goat. If you switch, you always get the other kind of reward.
Goats have no maintenance cost, moves your lawn for free and you can even get milk from them. Awesome creatures. :) | | You should always switch, as if you stick with your current one you have a 1 in 3 chance, whereas if you switch you then have a 1 in 2 chance :) | for Lord harddude:
STB has already explained :D
and also he has a good point about which one is better | | Yup thats right guys :) | for virtual_vitrea:
1800 rs |
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