What the heck...

1. Senior Member
Join Date
Dec 1969
Posts
96,118

## What the heck...

...since Mauricio is handing out some old "chestnuts" of logic problems, how about this one?<BR><BR>You are given several rolls of pesos and are told that they are all genuine *except* that one of the rolls contains only counterfeit coins.<BR><BR>You are also told that the counterfeit coins don&#039;t weigh the same as the other coins.<BR><BR>You are given a sensitive scale to measure the weights.<BR><BR>What is the *MINIMUM* number of weighings that you can perform to find out which roll contains the counterfeit coins *AND* discover whether they are lighter or heavier than the real coins.<BR><BR><BR>

2. Senior Member
Join Date
Dec 1969
Posts
96,118

## A variation on that...

Assume that, instead of a sensitive scale that can measure the weights, all you have is a balance scale. One with a pan on the left and a pan on the right, where usually you would put carefully measured weights on one side to balance the other. But in this case, the weights are missing.<BR><BR>*NOW* what is your answer?<BR><BR>And under what conditions is your answer correct?<BR><BR>

3. Senior Member
Join Date
Dec 1969
Posts
6,476

## Trick Question?

Or was there more to it?<BR><BR>Because I got lucky on first 2 i picked<BR>weighed them and left side was heavier..<BR>So remove the right side, and added one of the new rolls <BR>and then the weight was equal to the left one....<BR><BR>So since all rolls are equal except the counterfit one, then the lighter one (the on removed from the right) is the counterfit roll..<BR><BR>So what did I miss?<BR>;-)<BR>

4. Senior Member
Join Date
Dec 1969
Location
Posts
1,400

## I was using equations and estadistic, but...

Solution is simple as this... I imagine but I would&#039;t be able...

5. Senior Member
Join Date
Dec 1969
Posts
96,118

Sorry, I guess I should have said "What is the minimum number of weighings that will GUARANTEE that you will ALWAYS get the right answer?"<BR><BR>Forget the balance scale version for now. Just go for the first question.<BR><BR><BR>

6. Senior Member
Join Date
Dec 1969
Posts
6,476

And a trick answer...<BR><BR>Since there were variables left out, it requires a random answer...<BR><BR>How many Rolls do we have?<BR>And where in the "Picking order" does the counterfit show up?<BR>(Big difference if its the 5th or 10th roll)...<BR><BR>So because of that, it requires a random answer as shown...<BR><BR>http://www.links-golf.net/puzzle.asp<BR><BR>And yes, I gave the real answer your looking for there too.<BR>;-)<BR><BR>

7. Senior Member
Join Date
Dec 1969
Posts
10,852

## Seems too simple...

So I&#039;m probably missing something, as it seems I usually am these days. &#060;Grin /&#062;<BR><BR>However...My initial thought is that if you let x be the number of coin rolls, the answer is (x / 2) + 1 if x is even, and ((x - 1) / 2) + 1 if x is odd. <BR><BR>I&#039;ll have to give it more of a think later.

8. Senior Member
Join Date
Dec 1969
Location
Posts
1,400

## RE: What the heck...

Hey Billy,<BR><BR>What is your main page again, I know you have interesting stuff there...<BR><BR>

9. Senior Member
Join Date
Dec 1969
Posts
2,930

## i think i read it wrong...

so the minimum would be .. weigh one, weigh another, if they&#039;re different, weigh another (best case == minimum)... 3, maybe<BR><BR>nope, tried weighing 2 at the same time, still took me 3 weighs.<BR><BR>i guess i&#039;m assuming that the minimum would be if you got extremely lucky and one of the first three you weighed was the counterfeit roll.

10. Senior Member
Join Date
Dec 1969
Posts
6,476

## And what happens

with that equasion when you have 40 rolls,<BR>and the 5th one you test is the counterfit roll?<BR><BR>;-)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•