A frog can jump between three lily pads with equal probability of landing on any one. If the frog can only jump to a different lily pad, what is the probability that the frog will start and end on the same lily pad after three jumps?

*Solution to yesterday’s problem:*

For every red flower in a garden, there are three blue flowers. For every two blue flowers, there are five purple flowers. For every flower of these colors, there are six yellow flowers. If there are fifteen purple flowers, how many flowers are there in all?

If there are fifteen purple flowers, then there are six blue flowers by the second statement. Then there are two red flowers by the first statement. Then there are 23 total flowers, and 23 x 6 = 138 yellow flowers. Adding these up together, we find that there are *161 flowers* in this (apparently) large garden.

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