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Three ants are sitting at the three corners of an equilateral triangle.
Each ant starts randomly picks a direction and starts to move along the
edge of the triangle. What is the probability that none of the ants
collide?
'THIS' is the probability!
What was the problem?
Each ant can decide to go either clockwise or anti-clockwise. That is there are 2 options available for each ant to go. Hence, there will be total 2x2x2 = 8 possible combination of ants' different paths.
Now 2 ants won't collide if & only if all are either moving clockwise or anti-clockwise. In short, out of 8 possible combinations only 2 combinations are there where ants won't collide.
Hence, the probability that ant won't collide is 2/8 = 0.25.
A newspaper made of 16 large sheets of paper folded in half. The
newspaper has 64 pages altogether. The first sheet contains pages 1, 2,
63, 64.
If we pick up a sheet containing page number 45 what are the other pages that this sheet contains?
Here is the solution of puzzle!
What was the puzzle?
If the page starts with odd number 1 & back side followed by even 2 then at the back of page number 45, there must be number 46.
Generally, for the page p, page 65 - p shares the same sheet as p. Like page 1 and 65-1 =64, page 2 and 65-2=63 page are on the same sheet.
Therefore, page 45 must be on the same sheet as 65 - 45 = 20 page number. And the page 46 must be on the same sheet as page 65 - 46 = 19.
In short, the pages 19,20,45 and 46 must be on the same sheet.
