| Quiz 12 Golds |
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In 1989, when I studied at a university in Bandung, with my friends we tried to solve a quiz which was recieved from a Lecture. Let's see the quiz. 1. Introduction - I have 12 block of Golds in my hand. If we look at carefully, 12 gold are pure golds with same Color, same size, same shape etc.
- Unfortunately, one of them is not pure gold. we can not differ this one Gold. The only one way is by using Scale. Scale show one gold has different weight. It may be heavier or lighter than 11 others Gold. We don't know , only scale.
- the problem is : I just have to use the scale for 3 times. I can use the scale to compare such as : 1 Gold to 1 Gold , 2 Golds to 2 Golds, 3 Golds to 3 Golds, 4 Golds to 4 Golds, 5 Golds to 5 Golds or 6 Golds to 6 Golds. So, can you solve it ?
II. Solution I devide 12 Golds in to 3 Groups. Let say Group A, Group B, and Group C. ( use different color ) Group A : Group B : Group C :
* 1st Chance We use Scale as chance no.1
Result : 1. If they are Balance -> conclution all Golds in group A & all Golds in group B is Pure Gold. 1 Gold among Group C is not Pure Golds 2. If they are not Balance -> Conclution All Golds in Group C are Pure Golds. One Gold is among Group B and Group C is not pure Gold.
Let's go to Result no.1 that is If they are balance. We want to get 1 not pure Gold from Group C
* 2nd Chance So, We use Scale as chance no.2
Result : 1.1 If they are Balance -> conclution Gold no.9 and Gold no. 10 are pure Golds. Not pure gold may be No. 11, may be no. 12 1.2 If they are not Balance -> conclution it may Gold no.9 or Gold no. 10 not pure Golds. Gold No. 11 and Gold no. 12 are pure Gold.
* 3th Changes We use Scale as chance no.3
- Let's follow up result no. 1.1 : Compare Gold No.9 (Pure Gold) to Gold No.11 * If Result balance, conclution Gold No. 11 is pure , Gold No. 12 is not pure * If Result not balance, conclution Gold No. 11 is not pure , Gold No. 12 is pure
- Let's follow up result no. 1.2 : Compare Gold No.9 (Pure Gold) to Gold No.11 * If Result balance, conclution Gold No. 10 is pure , Gold No. 12 is pure * If Result not balance, conclution Gold No. 9 is not pure , Gold No. 10 is pure
Finish Result No.1 -> So How about Result No.2 ? -----------------------------------------
-> 2. If they are not Balance -> Conclution All Golds in Group C are Pure Golds. One Gold is among Group B and Group C is not pure Gold. This situation means that Golds in Group C are Pure Golds
-> we consider Group A is heavier than Group B. SO we do not know not pure Gold come from heavier one or from lighter one. Group A : consider heavier one
Group B : Consider lighter one
Group C : Pure Golds
Now, I create new Group : Group K : 3 pure Golds ( Group C) + 1 Gold (Group A) Group L : 2 Golds from Group B + 2 Golds from Group A Group M : 2 Golds from Group B + 1 Gold from Group A
* 2nd Chance So, We use Scale as chance no.2
Result : 2.1 If they are balance ( K & L) , conlution Group K and Gorup L are pure Golds. So, check Group M 2.2 If they are not balance (K & L ), conclution that one gold from Group K or Group L is not Pure Gold
Let's say they are balance, means pure Gold is no. 7 or no. 8 * 3th Chance So, We use Scale as chance no.3
with Gold No.8
Result : 2.1.1 If they are balance , means Gold no.7 and Gold no. 8 are Pure Golds 2.1.2 If they are not balance, mean the lighter one is not pure Gold. Why ? because this gold make Group A is lighter than Group B - Gold No.7 is lighter mean Gold No.7 is not pure Gold - Gold No.8 is lighter mean Gold No.8 is not pure Gold
Let's go to result 2.2 If they are not balance (K & L ), conclution that one gold from Group K or Group L is not Pure Gold. Result : 2.2.1 IF Group K is heavier than Group L (K > L) 2.2.2 IF Group K is lighter than Group L (K < L)
2.2.1 If Group K is heavier than Group L (K > L) means : It may Gold no.1 cause heavier or Gold no.5 or Gold no. 6 cause lighter. So compare Gold No.5 : Gold No.6 * 3th Chance
Compare Gold No.5 with Gold No.6
- If they are balance, Gold No.1 - If they are not balance, the lighter one is not pure Gold.
2.2.2 IF Group K is lighter than Group L (K < L) means : Gold no. 2 * 3th Chance
Compare Gold No.2 with Gold No.3
- If Gold No.2 - If Gold No.3
---- Finish ----
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