Assume you have nine coins, one of which is counterfeit and weighs less than the

Question

Assume you have nine coins, one of which is counterfeit and weighs less than the other eight coins. Diagram the least number of weighings required to absolutely determine which of the nine coins is counterfeit as a tree. Indicate a scale as a line with numbers on the left and right indicating the number of the coin being weighed. Under the scale indicate the number of the counterfeit coin in position with a circle around it. For example, weighing coins numbered one and two on the left and eight and nine on the right is diagrammed as:

Explanation / Answer

Make three set

Set 1:- 1, 2, 3 (coin numbered one two and three)

Set 2:- 4, 5, 6 (coin numbered four five and six)

Set 3:- 7, 8, 9 (coin numbered seven eight and nine)

Pick any two set and do Weighing:-

(Like here I pick set 1 and set 2)

1, 2, 3                         4, 5, 6

Then there are condition for either balanced or unbalanced

(Set 1==Set 2)

(Set 1 < Set 2)

(Set 1 >Set 2)

If balanced, then counterfeit coin will be in next Set 3

Took Set 3 and do Weighing

7                                                 8

If balanced, then counterfeit coin will be in numbered 9

If unbalanced then counterfeit coin will be that, whichever less weight of 7 and 8

If(7==8): counterfeit coin will be in numbered nine

If(7<8): counterfeit coin will be in numbered seven

(if7>8): counterfeit coin will be in numbered eight

If unbalanced, then counterfeit coin will be there, whichever less weight of set 1 and set 2

If (Set 1 < Set 2)                                                                                                        If (Set 1 > Set 2)

Then pick up set 1 for Weighing then pick up set 2 for Weighing

1                                  2                                                                     4                                             5  

If (1==2) counterfeit coin will be number three If (4==5) counterfeit coin will be number six

If (1 < 2) counterfeit coin will be number one                      If (4<5) counterfeit coin will be number four

If(1>2) counterfeit coin will be number two                        If   (4>5) counterfeit coin will be number Five

Minimum number of weighing required two

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Thanks a lot.

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