What do you think?

Chancie · 10-15-2010, 02:10 PM

My students obsessed about this problem today.

How would you solve it?

You have 100 valuable coins.

Well, one of the coins is counterfeit, so it’s not as valuable.

It’s either lighter or heavier than the genuine coins.

The only tool you have is a balance scale, and you have to pay a fee each time you use it.

How will you find the counterfeit coin?

Rockinonahigh · 10-15-2010, 02:24 PM

It depends if all the coins are of the same sise and ammout of value,some coins are made of diffent metals so weight is diffrent on each.
My soulution(sp?) would be to seprate all the coins to theire monatary amount value,then look at them very carefuly,then pick out the ones I think may not be real.Then drop them on the table one at the time till one dosent sound the same when it hits the table.Result is u dont need to use the scale at all to find the counterfit coin. u find the fake coin and save $$ not useing the scale.

Words · 10-15-2010, 02:32 PM

I'd invest $10 or so and go purchase another set of scales, one that didn't cost me money each time I used it.

Words

Chancie · 10-15-2010, 02:57 PM

Quote:

Originally Posted by Rockinonahigh

It depends if all the coins are of the same sise and ammout of value,some coins are made of diffent metals so weight is diffrent on each.
My soulution(sp?) would be to seprate all the coins to theire monatary amount value,then look at them very carefuly,then pick out the ones I think may not be real.Then drop them on the table one at the time till one dosent sound the same when it hits the table.Result is u dont need to use the scale at all to find the counterfit coin. u find the fake coin and save $$ not useing the scale.

The coins appear identical.

The only difference between the valuable real coins and the counterfeit coin is that

The fake coin is either heavier or lighter than the real coins.

Dreamer · 10-15-2010, 03:13 PM

Quote:

Originally Posted by Chancie

The coins appear identical.

The only difference between the valuable real coins and the counterfeit coin is that

The fake coin is either heavier or lighter than the real coins.

Okay my process of elimination and I am sure there is a better way but,
I would put 50 coins on each side of the scale, then take either the lighter or heavier side and divide them into 25 coins, if they weighed even then the counterfeit coin is amongst the other 25 coins, if they weighed uneven the counterfeit coin is amongst that 25. I would continue dividing the coins into equal amounts until I was left with only the counterfeit coin. Or you could just bite them and see if you were left with teeth marks

And if this makes no sense then I blame it on being aussie ty

Chancie · 10-15-2010, 03:13 PM

The difference between the real coins and the fake coin is too subtle to tell with your hands.

Your task is find a way to use the balance scale efficiently.

ETA: Dreamer and I posted at the same time.

Soft*Silver · 10-15-2010, 03:56 PM

I am horrible at these kind of problems but I love them.Please post the answer even if no one gets it!

LipstickLola · 10-15-2010, 04:06 PM

This might as well be the "one train leaves the NY station at 10 am doing 100 mph, one train leaves Chicago at 10 am doing 150 mph, what time do they intersect in.....Timbucktoo?"

theoddz · 10-15-2010, 04:44 PM

Ooooo.....I love love LOVE these kinds of problems!!!!

Wish I'd gotten in on this one a bit sooner.

~Theo~

.....loves puzzles and problem-solving exercises.

rlin · 10-15-2010, 05:19 PM

i imagine that halving them til you get to the winner is the better idea... if the scale has to be used and they are identical i believe that would be the best bet...
of course... i am sure that there must be something else that works better... because that just sounds too logical and easy...

Soft*Silver · 10-15-2010, 05:28 PM

Take 1 known genuine coin by weight. Divide the rest into 3 of 33 and weight them. The pile that is lighter or heavier gets cut into 3rds till you single it out.

JAGG · 10-15-2010, 05:39 PM

Well the question is ambiguous .If you have to pay each time you use the scale, does putting them on and then off count as one time or two? Also if you have to pay everytime you use the scale what's the goal here, what's the object of this quest? To spend the least amount of money possible in your quest, or is the goal to find out which coin is bogus? Anyway I have about 20 more questions because your details are not very clear. But here's my answer. Assumming putting all the coins on the scale counts as a one time use , and taking them all off counts as an additional use, I'd put all the coins on the scale. ( that's one time) Then I'd take them off one at a time, watching the scale for the difference in weights. (For example the first 15 I took off, all weighted 3 ounces each but the 16th one weighted 2 ounces, and the next 4 I took off weighted 3 ounces, I'd set the one that weightes 2 ounces aside) I'd set the different one aside and finished taking the other coins off, that would count as the second use of the scale. So 2 times I'd use the scale. If putting them on and off counts as one time use then I only used the scale once.

Gemme · 10-15-2010, 05:59 PM

Math is hard.

I'd bring them all to a coin dealer and let him or her sort it out.

Soft*Silver · 10-15-2010, 06:24 PM

nooooo... you have to use that scale!

Quote:

Originally Posted by Gemme

Math is hard.

I'd bring them all to a coin dealer and let him or her sort it out.

Gemme · 10-15-2010, 06:29 PM

Quote:

Originally Posted by softness

nooooo... you have to use that scale!

Make me.

*grin*

This is not my forte but I am interested in the best answer.

Chancie · 10-15-2010, 07:13 PM

Quote:

Originally Posted by JAGG

Well the question is ambiguous .If you have to pay each time you use the scale, does putting them on and then off count as one time or two? Also if you have to pay everytime you use the scale what's the goal here, what's the object of this quest? To spend the least amount of money possible in your quest, or is the goal to find out which coin is bogus? Anyway I have about 20 more questions because your details are not very clear. But here's my answer. Assumming putting all the coins on the scale counts as a one time use , and taking them all off counts as an additional use, I'd put all the coins on the scale. ( that's one time) Then I'd take them off one at a time, watching the scale for the difference in weights. (For example the first 15 I took off, all weighted 3 ounces each but the 16th one weighted 2 ounces, and the next 4 I took off weighted 3 ounces, I'd set the one that weightes 2 ounces aside) I'd set the different one aside and finished taking the other coins off, that would count as the second use of the scale. So 2 times I'd use the scale. If putting them on and off counts as one time use then I only used the scale once.

It's a balance scale, so you can compare coins in groups or singly.

And the idea is to be efficient.

Chancie · 10-17-2010, 11:08 AM

There are a few different ways to start this problem.

My students agreed that

They would divide the coins in four piles with 25 coins each, and

I labeled them A, B, C, and D.

First we compared A and B, and either

They balanced the scale, which meant that they were all valuable coins or

They were different, which meant that all the coins in C and D were genuine.

Gemme · 10-18-2010, 09:40 PM

Yay for Dreamer being the closest.

dreadgeek · 10-30-2010, 07:15 AM

Quote:

Originally Posted by Chancie

My students obsessed about this problem today.

How would you solve it?

You have 100 valuable coins.

Well, one of the coins is counterfeit, so it’s not as valuable.

It’s either lighter or heavier than the genuine coins.

The only tool you have is a balance scale, and you have to pay a fee each time you use it.

How will you find the counterfeit coin?

Okay, I'm probably going to show my ass here but I'm going to respond before I read anyone's responses:

I would take the coins, divide them into four equal groups then compare G-1, G-2, G-3 and G-4.

First iteration: compare G-1 and G-2. If equal then go to second iteration.
Second iteration: compare G-3 and G-4 at this point ONE of the piles will be unequal because the conterfeit coin has to be in one of those groups.

That's the most elegant solution I can come up with--at least while I wait for the coffee to finish brewing.

Chancie · 11-02-2010, 03:17 PM

That is very like what my kids came up with as a group.

We had already talked about something our old textbook called the guessing game algorithm, and

That algorithm is a lot like binary search.

So they hypothesized that it would be efficient to divide the coins into groups, and

They knew that it wouldn't be useful to divide the coins into two groups because

The still wouldn't know which pile contained the counterfeit and

They wanted something like a control, and

Having the control changed the way they searched after the first few iterations.

Anyway, it's worth noting that though the honors class came up with the naming system quickly and

They were able to predict some of the sticky places,

The other ninth grade class did very well at working together to solve this problem.

10-15-2010, 02:10 PM	#1
Chancie Senior Member How Do You Identify?: queer femme-inist Relationship Status: I'm lucky. Join Date: May 2010 Location: Western Mass Posts: 3,774 My Photo Gallery Thanks: 9,518 Thanked 14,542 Times in 2,744 Posts Rep Power: 21474855	What do you think? My students obsessed about this problem today. How would you solve it? You have 100 valuable coins. Well, one of the coins is counterfeit, so it’s not as valuable. It’s either lighter or heavier than the genuine coins. The only tool you have is a balance scale, and you have to pay a fee each time you use it. How will you find the counterfeit coin?

10-15-2010, 03:56 PM	#7
SoftSilver Infamous Member How Do You Identify?: femme Preferred Pronoun?: she Relationship Status: Married Join Date: Nov 2009 Location: rose cottage Posts: 5,592 My Photo Gallery Thanks: 8,948 Thanked 15,908 Times in 4,062 Posts Rep Power*: 21474857	I am horrible at these kind of problems but I love them.Please post the answer even if no one gets it! __________________ Pole bachit, a lis chuye. The field sees, the forest hears

10-15-2010, 04:06 PM	#8
LipstickLola Member How Do You Identify?: Happy Preferred Pronoun?: she Join Date: Sep 2010 Location: planet Earth Posts: 682 My Photo Gallery Thanks: 1,679 Thanked 1,597 Times in 433 Posts Rep Power: 5678217	This might as well be the "one train leaves the NY station at 10 am doing 100 mph, one train leaves Chicago at 10 am doing 150 mph, what time do they intersect in.....Timbucktoo?" __________________ Happiness......it's a choice!!

10-15-2010, 04:44 PM	#9
theoddz Senior Member How Do You Identify?: Cranky Old Poop Preferred Pronoun?: Mr. Beast Relationship Status: Married Join Date: Nov 2009 Location: Central Texas Posts: 3,537 My Photo Gallery Thanks: 11,111 Thanked 9,927 Times in 2,509 Posts Rep Power: 21474855	Ooooo.....I love love LOVE these kinds of problems!!!! Wish I'd gotten in on this one a bit sooner. *~Theo~* .....loves puzzles and problem-solving exercises. __________________ *"All that is gold does not glitter, Not all those who wander are lost; The old that is strong does not wither, Deep roots are not reached by the frost."* -- J. R. R. Tolkien

10-15-2010, 05:28 PM	#11
SoftSilver Infamous Member How Do You Identify?: femme Preferred Pronoun?: she Relationship Status: Married Join Date: Nov 2009 Location: rose cottage Posts: 5,592 My Photo Gallery Thanks: 8,948 Thanked 15,908 Times in 4,062 Posts Rep Power*: 21474857	Take 1 known genuine coin by weight. Divide the rest into 3 of 33 and weight them. The pile that is lighter or heavier gets cut into 3rds till you single it out. __________________ Pole bachit, a lis chuye. The field sees, the forest hears

10-15-2010, 02:24 PM	#2
Rockinonahigh Senior Member How Do You Identify?: stone butch Preferred Pronoun?: makes no diffrence,I know who I am. Relationship Status: single,maybe looking if the right person comes along. Join Date: Dec 2009 Location: shreveport,Louisiana Posts: 4,907 My Photo Gallery Thanks: 4,682 Thanked 14,933 Times in 3,938 Posts Rep Power: 21474856	It depends if all the coins are of the same sise and ammout of value,some coins are made of diffent metals so weight is diffrent on each. My soulution(sp?) would be to seprate all the coins to theire monatary amount value,then look at them very carefuly,then pick out the ones I think may not be real.Then drop them on the table one at the time till one dosent sound the same when it hits the table.Result is u dont need to use the scale at all to find the counterfit coin. u find the fake coin and save $$ not useing the scale.

10-15-2010, 02:32 PM	#3
Words Member How Do You Identify?: Queer femme submissive Relationship Status: Married Join Date: Nov 2009 Location: UK Posts: 969 My Photo Gallery Thanks: 1,449 Thanked 4,258 Times in 677 Posts Rep Power: 21474852	I'd invest $10 or so and go purchase another set of scales, one that didn't cost me money each time I used it. Words

10-15-2010, 03:13 PM	#6
Chancie Senior Member How Do You Identify?: queer femme-inist Relationship Status: I'm lucky. Join Date: May 2010 Location: Western Mass Posts: 3,774 My Photo Gallery Thanks: 9,518 Thanked 14,542 Times in 2,744 Posts Rep Power: 21474855	The difference between the real coins and the fake coin is too subtle to tell with your hands. Your task is find a way to use the balance scale efficiently. ETA: Dreamer and I posted at the same time.

10-15-2010, 05:19 PM	#10
rlin Member How Do You Identify?: human Join Date: Mar 2010 Location: nomad Posts: 712 My Photo Gallery Thanks: 1,450 Thanked 1,189 Times in 451 Posts Rep Power: 1004849	i imagine that halving them til you get to the winner is the better idea... if the scale has to be used and they are identical i believe that would be the best bet... of course... i am sure that there must be something else that works better... because that just sounds too logical and easy...

10-15-2010, 05:39 PM	#12
JAGG Infamous Member How Do You Identify?: Butch Preferred Pronoun?: JAGG Relationship Status: =) Join Date: Nov 2009 Location: Tulsa (cat free zone) Posts: 6,093 My Photo Gallery Thanks: 18,651 Thanked 17,531 Times in 4,137 Posts Rep Power: 21474858	Well the question is ambiguous .If you have to pay each time you use the scale, does putting them on and then off count as one time or two? Also if you have to pay everytime you use the scale what's the goal here, what's the object of this quest? To spend the least amount of money possible in your quest, or is the goal to find out which coin is bogus? Anyway I have about 20 more questions because your details are not very clear. But here's my answer. Assumming putting all the coins on the scale counts as a one time use , and taking them all off counts as an additional use, I'd put all the coins on the scale. ( that's one time) Then I'd take them off one at a time, watching the scale for the difference in weights. (For example the first 15 I took off, all weighted 3 ounces each but the 16th one weighted 2 ounces, and the next 4 I took off weighted 3 ounces, I'd set the one that weightes 2 ounces aside) I'd set the different one aside and finished taking the other coins off, that would count as the second use of the scale. So 2 times I'd use the scale. If putting them on and off counts as one time use then I only used the scale once. __________________ I don't want to spend my life with someone I can live with, I want to spend my life with someone I can't live without.

10-15-2010, 05:59 PM	#13
Gemme Practically Lives Here How Do You Identify?: Queer Stone Femme Girl of the Unicorn Variety Preferred Pronoun?: She, as in 'She's a GEM' Join Date: Nov 2009 Location: The roads are narrow here Posts: 36,631 My Photo Gallery Thanks: 182,498 Thanked 107,973 Times in 25,664 Posts Rep Power: 21474888	Math is hard. I'd bring them all to a coin dealer and let him or her sort it out. __________________ Gemme's Journal I'm misunderestimated.

10-17-2010, 11:08 AM	#17
Chancie Senior Member How Do You Identify?: queer femme-inist Relationship Status: I'm lucky. Join Date: May 2010 Location: Western Mass Posts: 3,774 My Photo Gallery Thanks: 9,518 Thanked 14,542 Times in 2,744 Posts Rep Power: 21474855	There are a few different ways to start this problem. My students agreed that They would divide the coins in four piles with 25 coins each, and I labeled them A, B, C, and D. First we compared A and B, and either They balanced the scale, which meant that they were all valuable coins or They were different, which meant that all the coins in C and D were genuine.

10-18-2010, 09:40 PM	#18
Gemme Practically Lives Here How Do You Identify?: Queer Stone Femme Girl of the Unicorn Variety Preferred Pronoun?: She, as in 'She's a GEM' Join Date: Nov 2009 Location: The roads are narrow here Posts: 36,631 My Photo Gallery Thanks: 182,498 Thanked 107,973 Times in 25,664 Posts Rep Power: 21474888	Yay for Dreamer being the closest. __________________ Gemme's Journal I'm misunderestimated.

11-02-2010, 03:17 PM	#20
Chancie Senior Member How Do You Identify?: queer femme-inist Relationship Status: I'm lucky. Join Date: May 2010 Location: Western Mass Posts: 3,774 My Photo Gallery Thanks: 9,518 Thanked 14,542 Times in 2,744 Posts Rep Power: 21474855	That is very like what my kids came up with as a group. We had already talked about something our old textbook called the guessing game algorithm, and That algorithm is a lot like binary search. So they hypothesized that it would be efficient to divide the coins into groups, and They knew that it wouldn't be useful to divide the coins into two groups because The still wouldn't know which pile contained the counterfeit and They wanted something like a control, and Having the control changed the way they searched after the first few iterations. Anyway, it's worth noting that though the honors class came up with the naming system quickly and They were able to predict some of the sticky places, The other ninth grade class did very well at working together to solve this problem.