For the next part do the same thing but with nine coins one

For the next part, do the same thing, but with nine coins, one of which is bad - still use 3 weighings. Finally, do it with 13 coins.

Solution

1)For 8

We can find the Bad one in 3 comparations by following steps

Divide these 8 coins into 4 groups

group[1]=[1,2]

group[2]=[3,4]

group[3]=[5,6]

group[4]=[7,8]

Then

Compare group[1] with group[2]

if group[1] has the same weight with group[2]

//now we know[1,2,3,4] are good

if group[1] with group[3]

if group[1] has the same weight with group[3]

//now we know[1,2,3,4,5,6] are good

Compare 1 with 7

if 1 has same weight with 7,then 8 is bad

else 7 is bad

else

// now we know the bad one is in[5,6] and wether if its heavier or lighter

if group[1] is heavier then group[3]//the bad one is lighter

compare 6 with 7, the lighter one is bad

else //the bad one is heavier

compare 6 with 7, the heavier one is bad

//now we know [5,6,7,8] are good

if group[1] is heavier then group[2]

compare group[1] with group[3]

if group[1] has the same weight with group[3]

//now we know the bad one is in[3,4]and the bad is lighter

compare 3 with 4, the lighter is bad

else//now we know the bad one is in[1,2]and the bad one is heavier

compare 1 with 2, and heavier is bad

compare group[1] with group[3]

if group[1] has the same weight with group[3]

//now we know the bad one is in[3,4] and teh bad one is heavier

compare 3 with 4, the heavier is bad

else//now we know the bad one is in[1,2] and the bad one is lighter

compare 1 with 2, the lighter is bad

2)For 9

we can find the bad one in 3 comparitions

divide these 9 into 4 groups

group[1]=[1,2] group[2]=[3,4] group[3]=[5,6] group[4]=[7,8,9]

Repeat the above steps as usally and replace group[4]=[7,8,] with group[4]=[7,8,9]

3)For 13

same for 13 in 3 comparations

group[1]=[1,2,3]

group[2]=[4,5,6]

group[3]=[7,8,9]

group[4]=[10,11,12,13]

Repeat the above steps as usally and replace groups with above values