2 easy math riddles

[coke]

2 easy math riddles... i know the answers but i'm not telling!

 

1) You are using the scales on the left picture...

 

You have 9 coins. One of them is fake and weighs lighter then the other ones. After using the scales only twice, how do you figure out which coin is fake?

 

2) You are using the scales on the right picture (with exact amount)...

 

You have 10 stacks with 10 coins each. 9 of the stacks are real, and contain coins that weigh 1 gram each. 1 of the stacks is fake and contains coins that weigh 1.1 grams. After using the scales only once, how do you find the fake stack?

[Sisyphus]

For the first one, just weigh 3 vs. 3. This will narrow it down to 3 choices (whichever side is lighter, or the 3 you didn’t weigh if it comes out even). Then of those 3, weigh 1 vs. 1. Again, whichever is lighter, or the remaining one if they’re even.

 

For the second, arrange them so that each side has a different number of coins for each stack. So, put the first stack 10 on the left and 0 on the right, the next 9 on the left and 1 on the right, etc. Then, when you weigh them, which side is heavier and by how much will tell you the distribution of the lighter coins. For example if the left side is 1 gram heavier, you know it was the first stack. If 0.8 grams heavier, you know it was the second. Etc.

 

Bam! Easy.

[coke]

yes... too easy

[lakmilis]

ye.. already answered

[Patrick Henry]

Heard that one from a friend... answer above.

[sideline]

got Answered...

[coke]

It's all sisyphu's fault .

It was supposed to be an interesting problem.

 

nah, way too easy problem.

Edited April 5, 2009 by coke
nah this problem was too easy

[SFNfan#1]

For the second, arrange them so that each side has a different number of coins for each stack. So, put the first stack 10 on the left and 0 on the right, the next 9 on the left and 1 on the right, etc. Then, when you weigh them, which side is heavier and by how much will tell you the distribution of the lighter coins. For example if the left side is 1 gram heavier, you know it was the first stack. If 0.8 grams heavier, you know it was the second. Etc.

 

Bam! Easy.

 

I'm trying to understand your explanation but I guess I don't really understand how that scale works because it's shaped like abnormally for a certain reason I'm guessing.

[coke]

Ok, Sfnfan,

 

He decided to use the first scale, which is not a good idea, but I didn't bother correcting him...

 

Use the second scale which gives you an exact weight (i.e. 5.8 grams)

 

You have 10 stacks with 10 coins each. 9 of the stacks are real, and contain coins that weigh 1 gram each. 1 of the stacks is fake and contains coins that weigh 1.1 grams.

 

So, what you do is, put 10 coins from the first stack, 9 coins from the second stack, 8 coins from the third stack...etc. etc. etc. 2 coins from the ninth stack ad 1 coin from the tenth stack onto the scale.

 

If all the stacks were real, you have 55 coins on there, so the scale should read 55 grams. But say if the first stack was fake, it would be offset by .1 grams for every coin, and you have 10 coins from the first stack, thus it would read 56 grams. If the tenth stack was fake, you only have 1 coin from the tenth stack, so it would read 55.1 grams. Depending on how much the weight is offset by, you can tell which stack was fake.

[SFNfan#1]

^^Clever Indeed.

Thanks for explaining it the long way.

[hemantc007]

I got the answer for both ones

 

in the first one you have to make 3 sets of 3 coin ...it is same as the above mentioned

 

in the second you have to make sets of coin as eg :- let one be stack "a" other be "b"similarly ther will be a,b,c,d,e,f,g,h,i,j

then make 2 set , in which first has 9 coin of a =A9, similarly series will be

A10 , B9 , C8 , D7 , E6 , F5 , G4 , H3 , I2 , J1 total mass =55g

and similarly other series

B 1, C2 , D3 , E4 , F5 , G6 , H7 , I8 , J9 total mass = 45g

 

now weigh them on the machine ( any one of the above series) then you will know that which one is fake due to amount of mass increase ........for eg in first series if total mass is 55.8g that mean the c stack is the fake one.......

 

quite easy one .........!!!!!!!!!!!!!!!!!!

[pjl83]

very good.

[hemantc007]

is it correct, i mean my method

 

 

thanks

[Fuzzwood]

I got the answer for both ones

 

in the first one you have to make 3 sets of 3 coin ...it is same as the above mentioned

 

in the second you have to make sets of coin as eg :- let one be stack "a" other be "b"similarly ther will be a,b,c,d,e,f,g,h,i,j

then make 2 set , in which first has 9 coin of a =A9, similarly series will be

A10 , B9 , C8 , D7 , E6 , F5 , G4 , H3 , I2 , J1 total mass =55g

and similarly other series

B 1, C2 , D3 , E4 , F5 , G6 , H7 , I8 , J9 total mass = 45g

 

now weigh them on the machine ( any one of the above series) then you will know that which one is fake due to amount of mass increase ........for eg in first series if total mass is 55.8g that mean the c stack is the fake one.......

 

quite easy one .........!!!!!!!!!!!!!!!!!!

 

Jup it is.

[hemantc007]

what is suppose to mean by "jup it is " , because i am new in short forms of the english language , used for chating............

plz............

[the tree]

what is suppose to mean by "jup it is "

"Yes, it is."

[iNow]

In spanish, the letter "J" often sounds like the letter "Y," so just pretend he said "Yup" or "Yep," and that he meant "Yes."

[Kyrisch]

In spanish, the letter "J" often sounds like the letter "Y," so just pretend he said "Yup" or "Yep," and that he meant "Yes."

 

Actually, the letter 'y' sounds like the letter 'j'. The letter 'j' sounds like the letter 'h'. So it's kind of a reverse substitution.

[Fuzzwood]

"it is" should be a dead give-away anyway.

[hemantc007]

thanks for help.........

[Lkreyna2]

measure 4 coins on each side for the first problem, but put in the coins one by one and look at the scale after placing 1 coin on both sides.