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Here's a famous riddle you may have seen before:

 

There is an island with 12 islanders. All of the islanders individually weigh exactly the same amount, except for one, who either weighs more or less than the other 11.

You must use a see-saw to figure out whose weight is different, and you may only use the see-saw 3 times. There are no scales or other weighing device on the island.

How can you find out which islander is the one that has a different weight?

 Jan 6, 2019
 #1
avatar+701 
+1

I can't do it with 3 uses of saw, but I can do it with 4 uses of the see-saw. 

 

There are 12 people. A,B,C,D,E,F G H I J K, and #. Let's assume # is the odd one. Since we do not know if # is heavier or lighter than the others, this makes it a tad bit harder. 

 

1) Divide the 12 people into two groups. A - F and G - #. We measure one of the groups, 3 on one side and 3 on the other. Let's just say we measure ABC to DEF. If they are equal, that means the odd duck is in the second group. If they are not even, we go to step 2. For our purpose, let's assume Group 2 has the odd one, the #.

 

2) Choose 4 of the 6 from the group and measure them. Let's just say we measure GH and IJ. If they are equal, then the odd duck is in the group of 2. If they are not equal, then the odd duck is inside the group of 4.

 

3) a) If the group has 2 people, in our case K and #, we choose K or # and measure it with one of the normal ones. In our case, let's measure K and G. If they are equal, then the non-measured one (#) is the odd duck, but if they are not equal, then the one that was chosen to be measured with the normal one, in our case K, is the odd duck.

 

3) b) If the group has 4 people, randomly choose 2 people and take them out. Let's make a new scenario, where the group of 4 is I, J, K and #. We randomly choose out K and #. We measure I and J. If they are equal, the odd one is either K or #, which we can find by using step 2 above. If I and J are not equal, then do as above in step 2.

 

4) More of step 2. The 4th step is only needed in some scenarios. 

 

- PM

 

P.S. please send the link to the solution...I want to know a quicker way. wink

 #2
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Assume one is heavier than the rest:

 

1 - First weighing. Put 6 on one side of the see-saw and the other 6 on the other side. Whichever side sinks or goes down, that side has the heaviest person.

 

2 - Second weighing. Split those into 3 and 3 and whichever side sinks, that side has the heaviest person.

 

3- Third weighing. Of those 3, weigh 2 of them. if the see-saw sinks, then that is the heaviest person. If the see-saw balances, then the remaining person is the heaviest.

 Jan 6, 2019
 #3
avatar+102447 
+1

Hi guest. Your method assumes that the odd person out is heavier than the others.

This may not be the case. The odd person out might be the lightest one. 

Melody  Jan 6, 2019
 #4
avatar+102447 
+1

 I do not need to use the see saw at all.

I did a visual inspection and noticed that 11 were small children and one was a huge adult.

So I decided that the adult was the odd one out.   :)

 Jan 6, 2019
 #6
avatar+24 
+1

Nice answer

asdf1243  Jan 6, 2019
 #5
avatar+24 
+1

Start by dividing the islanders into 3 groups of 4. Placing two groups results in two possible outcomes. 

 

(1) If they balance, they are all real. That means one of the remaining is more or less.

 

Weigh 3 of the regular weighing guys against 3 of the remaining ones. If they balance, the last guy is more or less. 

 

If it is lighter, one of the ones on the seesaw must be less. Weigh 2 of the suspicious ones. If they balance, then the third guy is less. If they don't balance, the lighter one is the guy we are looking for.

 

If it is heavier, one of the ones on the seesaw must be more. Weigh 2 of the suspicious ones. If they balance, then the third guy is more. If they don't balance, the heavier one is the guy we are looking for.

 

(2) If at first they don't balance, the remaining 4 are real. Replace 3 of the ones on the "heavier" side with 3 of the ones on the "lighter" side and add 3 real guys on the "lighter" side. If the same side is still heavier, it means that either the one that wasn't replaced on the "heavier" side is heavier or the one not replaced on the "lighter" side is lighter. Choose either of them, and weigh them against a real guy.

 

Also, if they balance at the second use, then one of the three "lighter" ones were fake. Weigh two against each other, If they balance, then the third guy is fake. If they don't balance, the lighter one is the guy we are looking for.

 Jan 6, 2019
 #7
avatar+18439 
0

place 6 on each side of the see-saw....    Pick the lighter side 6

 

Now place 3 on each side     Pick the lighter side 3

 

place one on each side.....    Like guest said, if they balance , then the islander NOT on the see saw is the lightweight......if they do NOT balance, the lightweight is up in the air.      Done.

 Jan 6, 2019
 #8
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+1

EP, the odd one out might be the heavy one. 

Guest Jan 6, 2019
 #10
avatar+101804 
+1

Put 6 people on one side of the see-saw and 6 on the other

 

Obviously....the heavy person will be on the lower side

 

Divide this side into two groups of 3......again...the heavy person will be on the lower side

 

Choose any 2 of these 3 people to weigh

 

We have two possibilities for the third weighing :

 

1) They balance.....the heavy person is the one not weighed

 

2) The don't balance....again....the heavy person is on the lower side

 

 

cool cool cool

 Jan 7, 2019
 #11
avatar+102447 
+1

But Chris you have still assumed that a person is heavier than all the others, just as EP assumed the opposite.

We do not know if the odd person is too heavy or too light. :/

 

I am sure some of the other answers are excellent but i have not wrapped my head around them yet.

 

I still like my answer though.  cheeky

Melody  Jan 7, 2019
 #12
avatar+101804 
0

Ah....I didn't see the "more or less" clause....!!!

 

cool cool cool

CPhill  Jan 7, 2019
 #13
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OK., so we have these twelve islanders,

Andy, Barry, Cliff, Darius, Ernie, Frank, Geoff, Harry, Isaac, Jacob, Kevin and Larry.

Eleven of them have the same weight but the twelfth, and we don't know which, is either lighter or heavier than the others.

We have to find the odd one out by the use of a see-saw which we are allowed to use just three times.

We let them take turns as follows.

First go         { Andy, Barry, Cliff, Darius}     V    {Ernie, Frank, Geoff, Harry}

Second go    {Andy, Harry, Kevin, Darius}   V    {Isaac, Frank, Jacob, Cliff}

Third go        { Isaac, Barry, Geoff, Harry}    V    {Larry, Darius, Frank, Jacob}

By noting what happens at each turn we can always work out which is the odd one out and whether he's 

lighter or heavier.

BTW., don't confuse Barry, Harry and Larry, it mucks up the whole thing if you do.

 

Here's an example of how its works, (though there are a number of variations in the reasoning).

Suppose that Ernie is heavier than the others.

What will happen is that at the first go, the right hand side will go down.

That means that either one of Andy, Barry, Cliff or Darius is lighter, or one of Ernie, Frank, Geoff or Harry is heavier.

At the second go, the see-saw will balance.

That means that they are all of the same weight and can be removed  from the 'first go' list.

We are left with either Barry being light or one of Ernie or Geoff being heavy.

At the third go they balance again so that lets us remove Barry and Geoff.

We are left with Ernie being the heavy one.

 

Here's three others to try.

(1) Left down, Left down, Balance.

(2) Balance, Left down, Right down.

(3) Right down, Right down, Left down.

 

Tiggsy

 Jan 7, 2019

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