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
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:
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?