CBSE BOARD XII, asked by devendraofficialdoc, 5 months ago

there is a pile of twelve dice,all of equl 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 in which you can find odd dice and determine if it is heavier or lighter,and how do you go about doing this?​

Answers

Answered by Nylucy
68

Answer:

My proposed solution:

1. Divide the 12 coins in groups A, B and C of 4 coins each. Let's denote them with { G }_{ A4 }, { G }_{ B4 } and { G }_{ C4 } [G for group and A, B and C groups of 4 coins each].

2. Take { G }_{ A4 }, { G }_{ B4 } and weigh them. [Measurement 1]

Scenario 1. If they weigh the same, the unequal coin is in { G }_{ C4 }

Scenario 2. If they weigh different, the coin is in these two groups only. Discard { G }_{ C4 }.

3. If Scenario 1==true, take first three coins from { G }_{ C4 }. Let's denote them by C1, C2 and C3. Weigh them against 3 coins from { G }_{ A4 } i.e. A1, A2, A3. [Measurement 2]

i. If {A1,A2,A3}=={C1,C2,C3}, the unequal coin is C4.

Weigh C4 against A1. [Measurement 3]

If heavier, C4 is heavier than all other 11 coins and if lighter, C4 is lighter than other 11 coins, of course.

ii. If {A1,A2,A3}!={C1,C2,C3}

a. {A1,A2,A3}>>{C1,C2,C3}

Make two parts

{C1,A1} and {C2,A2}. Weigh them [Measurement 3]

If {C1,A1}>>{C2,A2}; C2 is lighter than all other coins

If {C1,A1}<<{C2,A2}; C1 is lighter than all other coins

If {C1,A1}=={C2,A2}; C3 is lighter than all other coins

b. {A1,A2,A3}<<{C1,C2,C3}

Make two parts

{C1,A1} and {C2,A2}. Weigh them [Measurement 3]

If {C1,A1}>>{C2,A2}; C1 is heavier than all other coins

If {C1,A1}<<{C2,A2}; C2 is heavier than all other coins

If {C1,A1}=={C2,A2}; C3 is heavier than all other coins

4. If Scenario 2==true;

a. { G }_{ A4 }>>{ G }_{ B4 } [Measurement 2]

Take 3 coins from each group.

If {A1,A2,A3}=={B1,B2,B3}, the unequal coin is either A4 or B4.

Then weigh {A1,A4} against {B1,B4} [Measurement 3]

If {A1,A4}>>{B1,B4}; A4 is heavier than all other coins

If {A1,A4}<<{B1,B4}; B4 is heavier than all other coins

Similarly it can be found out for lighter coins from { G }_{ A4 } and { G }_{ B4 }.

For other possibilities, please follow 3.ii.a and 3.ii.b. Those situations and solutions are the same. Only you need t change the group name.

Hope this complies to all constraints.

Original answer here:

Answered by Anonymous
22

there is a pile of twelve dice,all of equl 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 in which you can find odd dice and determine if it is heavier or lighter,and how do you go about doing this?

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