Brain teaser see detail below?

Question

Victims of a shipwreck were lost at sea. Due to strong waves th ey were all soon separated. Search parties quickly went out to find them. On the first day 1/6 of the survivors were found. The next day 1/5 of those still lost were found. On the third day 1/4 of those still lost were found. On the fourth day 1/3 of those still lost were found. 1/2 of those still lost were found on the fifth day, and on the sixth and last day the 3 remaining boatmen and boatwomen were found.

How many people were originally lost at sea?

Answer 1

It's probably easiest to work backwards with this problem.  If on the 6th day there were 3 people, then on the 5th day there had to be 3*(2/1) = 6 people.  Continuing backwards, on the 4th day there were 6*(3/2) = 9 people, on the 3rd there were 9*(4/3) = 12, on the 2nd there were 12*(5/4) = 15, and on the first day there were 15*(6/5) = 18.  Therefore, there were 18 people originally lost at sea.  The clever way to do the problem is to realize that the way it is set up, the exact same number of people must have been found every day, so the total number of people must immediately be 3*6 = 18.

Answer 2

3 were 1/2 of 6

6 were 2/3 of 9

9 were 3/4 of 12

12 were 4/5 of 15 and

15 were 5/6 of the original 18.

Answer 3

You started with 18 boatmen.

Day 1:  1/6 (3 boatmen) were found leaving 15.

Day 2:  1/5 (3 boatmen) were found leaving 12.

Day 3:  1/4 (3 boatmen) were found leaving 9.

Day 4:  1/3 (3 boatmen) were found leaving 6.

Day 5:  1/2 (3 boatmen) were found leaving 3.

Day 6:  Last 3 boatmen were found.

Answer:

18 boatmen

Answer 4

18

Answer 5

8

Answer 6

3*(1-1/2)^-1=6

6*(1-1/3)^-1=9

9*(1-1/4)^-1=12

12*(1-1/5)^-1=15

15*(1-1/6)^-1=18

How many people were originally lost at sea? 18