Agnishom's original writeup:
An ant climbs down an ant-hill, going right or left as he moves down. In each cave, there are a number of sugar cubes available as indicated in the diagram.
Naturally, every ant wants to find the path from the top hill to one of the bottom hill along which he could collect the maximal number of sugar cubes.
An ant is climbing down an ant-hill, going right or left at each level. In each circular cave, there are a number of sugar cubes available as indicated by the numbers in the circle.
Naturally, every ant wants to find the downward path along which they could collect the maximal number of sugar cubes.
at every step, going to the cave that has the larger of the two sugar cubes will eventually give the largest number of sugar cubes he could possibly get.
An ant climbing down an ant-hill can choose to go either down and to the right or down and to the left at each level until it reaches the bottom of the hill. And at each junction, the ant collects a number of sugar grains indicated by the numbers in the circle.
Being greedy, this ant believes that if it always moves down towards the larger of the two values directly below, it will be able to collect the largest number of sugar grains overall. With the hill as shown above, is this greedy strategy optimal for collecting sugar?