Find the Lightest Bag: Min Weighings Needed

  • Thread starter Werg22
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In summary, if you have two balls that are the same color and you put them into different bags, you can determine the bag that has the lighter ball by doing two weighings.
  • #1
Werg22
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Interesting problem

Five bags each contain 10 balls. The first bag has yellow balls, the second blue balls, the third red balls, the fourth green balls and the fifth orange balls. All the balls in four of these bags (we don't know which ones) weigh 20 units each and the the balls in the remaining bag weigh 18 units. If we are to determine the bag containing the lighter balls by method of weighing on a single plate scale, what is the minimum number of weighings needed? Describe the procedure.
 
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  • #2
easy

take 1 ball from the first bag , 2 from the second, 3 from the third, get the pattern?

Weigh the lot of them, bag number = (300 - weight)/2
 
  • #3
This problem is well known I assume (not to take away any credit from you, Integral). I've came with this variation: if we're only allowed to take out 1 ball from each bag, what would be the minimum number of weighings?
 
  • #4
Werg22 said:
This problem is well known I assume (not to take away any credit from you, Integral). I've came with this variation: if we're only allowed to take out 1 ball from each bag, what would be the minimum number of weighings?

Then you have 5 balls (A,B,C,D,E) and one of them is different.
A binary search will find the ball in 3 weighings (maximum).
But sometimes, just 1 weighing will be enough.
So, the minimum is 1 weighing.

Ex:
Weigh ABCD . If ABCD=80, then "E" is the ball. If ABCD=78, then weigh AB.
If AB=40, then weigh C. If C=20 , D is the ball (and if C=18...)
If AB=38, then weigh A. If A=20, B is the ball (and if A=18...)

:smile:
 
  • #5
Rogerio said:

Then you have 5 balls (A,B,C,D,E) and one of them is different.
A binary search will find the ball in 3 weighings (maximum).
But sometimes, just 1 weighing will be enough.
So, the minimum is 1 weighing.

Ex:
Weigh ABCD . If ABCD=80, then "E" is the ball. If ABCD=78, then weigh AB.
If AB=40, then weigh C. If C=20 , D is the ball (and if C=18...)
If AB=38, then weigh A. If A=20, B is the ball (and if A=18...)

:smile:

Good, but I didn't say that you can't add a ball to bag.
 
  • #6
Werg22 said:
Good, but I didn't say that you can't add a ball to bag.
Well,in this case, 2 weighings will be the minimum necessary to ever determine the bag.
Put 1 ball "A" into the bag "B" , and 1 ball "C" into the bag "D".
Weigh the bags "B" + "D".
If B+D=440 then "E" is the bag. If not, weigh bag "B" .
Now, if B+D=438 and B=220 , then "C" is the bag.
If B+D=420 and B=220 , then "D" is the bag.
Etc...

:smile:
 
  • #7
Note: On the new skins, the color tag for spoilers is #e9e9e9 or #black (depending on browser...I think).

Also, do not quote spoiler posts.
 

What is the purpose of finding the lightest bag?

The purpose of finding the lightest bag is to determine the bag that weighs the least out of a group of bags. This can be useful in various situations, such as packing for a trip or shipping items with weight restrictions.

What is the minimum number of weighings needed to find the lightest bag?

The minimum number of weighings needed to find the lightest bag will depend on the number of bags and the weighing method used. However, in general, the minimum number of weighings will be log2(n) where n is the number of bags.

What is the best weighing method to find the lightest bag?

The best weighing method to find the lightest bag will also depend on the number of bags and the weighing equipment available. In general, if there are a large number of bags, a balance scale or a digital scale will be the most efficient weighing method.

How do you ensure accurate results when finding the lightest bag?

To ensure accurate results when finding the lightest bag, it is important to use a precise and calibrated weighing equipment. The bags should also be weighed in the same conditions, such as on the same surface and at the same temperature.

Can any bag be the lightest bag?

Yes, any bag can be the lightest bag depending on the weight of the items inside. It is possible for a larger bag to be lighter than a smaller bag if the items inside the larger bag are lighter than the items inside the smaller bag.

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