There is a collection of 12 balls of same color and weight except one ball of different weight. By using only a weighing balance ( with two pans) without weights,find the odd ball from the lot.Also determine if the odd ball is heavier or lighter than the rest.Only three weighments are allowed.
There is rectangular field ABCD.Sides AB and CD measure 600 ft;BC and AD measure 900 ft. A dog at corner A spots a rabbit at corner B and starts running at 30 mph to catch it.Simultaneously,the rabbit starts running away at 24 mph to a safe refuge at corner C. The dog keeps aim at the rabbit during the chase.
1. Will the dog be able to catch the rabbit before it reaches the safe refuge?
2. What would be the shape of its path and it's precise mathematical formula?
3. Is there a better path the smarter dog would have chosen?
Only by actually drawing the path in small segments I have tried to solve the problem.I would appreciate if someone could do the appropriate math.