Question

There is a pile of twelve dice, all of equal size, shape, colour, texture etc.

Eleven dice are of equal weight.

One dice is of a different weight.

What is the minimum number of readings (on a beam balance ) in which you can

find the "ODD" dice AND determine if it is heavier or lighter, and how do you go

about doing this?​

Answer 1

Given : a pile of twelve dice, all of equal size, shape, colour, texture etc.

Eleven dice are of equal weight.

One dice is of a different weight.

To Find :  minimum number of readings (on a beam balance ) in which you can find the "ODD" dice AND determine if it is heavier or lighter,

Solution:

Divide 12 into 3 groups

4 , 4 , 4

Take any two group  4 , 4

If they are equal  then  take one of them

and weigh with 3rd Group

if 3rd group is heavy then odd one is heavy

if Lighter then odd one is lighter

if 1st weigh are not equal

Then choose any one Heavier or lighter

if taken Heavier

and weighed with 3rd group and still Heavy

then odd one is heavy  

if Equal with 3rd group then odd one is Lighter

After Two weighing we know

Which group has odd one and  whether its heavier or lighter

Now Take  2 from  that  odd group and weigh

if found heavier  and lighter - u got final answer

if Equal then weigh Remaining  and found heavier  and lighter

Hence  2 Weighing required to determine whether odd one is lighter or heavier

and maximum two more to find odd one dice

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