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## Question

You have 10 packets of cigarettes and each packet contain 10 cigarettes. We assume that the packets are weightless and that each cigarette weigh 10 grams. There is a packet within the lot where each cigarette weights 1 gram less i.e. 9 grams. What is the minimum times you must weigh to find out which packet is the one with the lesser weight cigarettes ???

## 22 answers to this question

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0...If we are allowed to open the packets instead of weighing them, then the packet with 9 cigarettes will weigh 9 grams.

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5 times - stick them on a balance two at a time. Once you find the pair which is not balanced you will know which one is the lighter one.

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4 or 6

first weigh 5 and 5

take the 5 that weigh less and weigh two and two if they are equal you have found you light pack.

If they are not equal the wiegh the two that are lightest.

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0...If we are allowed to open the packets instead of weighing them, then the packet with 9 cigarettes will weigh 9 grams.

One packet had each cigareete weighing 9 grams each, so that pack weighed 9x10 = 90 grams instead of 100 grams

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3 or 2 if the second weighing equals out

5v5

2v2

1v1

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You have 10 packets of cigarettes and each packet contain 10 cigarettes. We assume that the packets are weightless and that each cigarette weigh 10 grams. There is a packet within the lot where each cigarette weights 1 gram less i.e. 9 grams. What is the minimum times you must weigh to find out which packet is the one with the lesser weight cigarettes ???

You need to weigh 4 or 6 times.

First 5 vs. 5 (2 times)

Lightest of this goes on

2 vs. 2 with one not being weighed (2 times)

If these are the same weight, you know that the packet that wasnt weighed is the lightest. If not, weigh the two packets and find which is the lightest (2 times)

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Only 1 time if you use a scale! Take 1 from the first pack, 2 from the second, 3 from the third and so on for all ten packs. Weigh all 55 cigs at the same time(1+2+3..+10=55). If they were all 10 grams, it would wiegh 550 grams, but one pack was 1 gram off per cig. So if the total weight is 1 gram from 550, then it's the first pack, if 2 grams from 550, the second pack, 3grams from 550, the third and so on!

I got it

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once.

stack the cigarettes up on the scale and take each pack off one at a time. you'll know if you grabbed the light pack when the scale reads a multiple of 10.

Edited by initialj

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only once with or without scale put 5 in one hand and 5 in the other or use a balance thingy the pack will obviously be much lighter than the rest.

You have 10 packets of cigarettes and each packet contain 10 cigarettes. We assume that the packets are weightless and that each cigarette weigh 10 grams. There is a packet within the lot where each cigarette weights 1 gram less i.e. 9 grams. What is the minimum times you must weigh to find out which packet is the one with the lesser weight cigarettes ???

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weighing once and simple math would do the charm (solution works for any # for packets)

Just arrange them in sequence and pick 1 cigarette from first, 2 from second and so on. now weigh only once and note down the value. Now (n/2)(n+1)(weight of each packet) gives the total weight if all packets were of same correct size. The total weight minus the weighed number gives u the packet #.

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Only 1 time if you use a scale! Take 1 from the first pack, 2 from the second, 3 from the third and so on for all ten packs. Weigh all 55 cigs at the same time(1+2+3..+10=55). If they were all 10 grams, it would wiegh 550 grams, but one pack was 1 gram off per cig. So if the total weight is 1 gram from 550, then it's the first pack, if 2 grams from 550, the second pack, 3grams from 550, the third and so on!
I got it

actually it's .1 gram off

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2 times at least, 3 times at most, if you are using the kind of scale that will balance the 2 sides and let you see which one is more and which is less.

weigh 5 packs on each side of the scale, take the 5 packs that are lighter, put one pack of the 5 you now have aside. now weigh 2 packs on each side of the scale. if the 2 packs balance, then the one you put aside is the lighter pack. if one side is lighter, weigh those two packs against each other to determine which is the lighter pack.

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actually it's .1 gram off

Why .1? They are 1 gram lighter, so 1 gram for each.

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Once.

First, label the box with number 1, 2, 3, .....,9, 10

Take 1 cigarette from box 1

Take 2 cigarettes from box 2

Take 3 cigarettes from box 3

and so on..

Take 10 cigarettes from box 10

Weigh all these together.

If all are weigh 10 grams each, the total weight should be 550 (1+2+3+...+10)*10 = 550

Since there is a box with 9 gram each. So

If the total weight = 549, then box 1 is lighter

If the total weight = 548, then box 2 is lighter

If the total weight = 547, then box 3 is lighter

and so on....

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could you specify what tool could be used for weighing:

1. accurate weighing-machine with a single pane (eg. with display showing the exact weight)

2. an old pair of scales (2 panes to compare 2 groups of cigarettes)

if you meant the first one, then it is already posted - check Weighing I. ... I have dedicated one whole page to such Weighing Puzzles

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I have a packet of 10 Marlboros in my left hand and a packet of 10 Lucky Strikes in my right hand. Which is the lighter of the two?

Neither, the lighter's in my pocket

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I have a packet of 10 Marlboros in my left hand and a packet of 10 Lucky Strikes in my right hand. Which is the lighter of the two?

Neither, the lighter's in my pocket

Showing a bit of age octopuppy. Do they still do Players Weights, ... so just look at the packet - ha ha !!

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I have a packet of 10 Marlboros in my left hand and a packet of 10 Lucky Strikes in my right hand. Which is the lighter of the two?

Neither, the lighter's in my pocket

Also the luck's may be filterless which may weigh less as I never came across a filterless marlboro.

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one time only.

take 1 cig from 1st pkt

2 cig from 2 pkt

3 cig from 3 pkt

.

.

.

.

then weigh

from the wt you calculate easily.

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this is probably wrong but if by chance you managed to select the lighter packet at random and weighed it, then it would only take a minimum of one weighing

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Why .1? They are 1 gram lighter, so 1 gram for each.

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It seems the OP has abandoned this thread. Not only not letting anyone know if they've answered correctly, but not answering rookie1ja when he asked if this is a variation of a riddle already on the site. I'm going to assume it is.

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