Philosopher Bob exercises every morning. He does steps up a flight of emergency stairs leading to the second floor egress door from the courtyard of his apartment high-rise. He first does single steps to the top, descends, runs up the flight, descends, then he takes the steps two at a time and comes down. Set done. He does ten of these for a good aerobic workout. But there’s a reason why he varies his routine in one set, other than for mere variety. Being such a deep thinker, especially when doing rote exercises, he tends to forget mundane things, like how many repetitions he’s done. In fact, he is so deep, he can’t remember past one. If he did the same single-step climbs twice in a row, he would actually lose track of how many he did! What a brilliant guy! But this problem also applies to how many sets he’s done. To help him keep track, when he finishes a set, he can place little white stones (all identical) on a knee-high brick wall surrounding a well landscaped garden near the steps, thus keeping count.

Question: What is the least number of stones Bob needs to put on the brick wall to keep count in a ten-set workout? Explain.

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## Shakeepuddn

Philosopher Bob exercises every morning. He does steps up a flight of emergency stairs leading to the second floor egress door from the courtyard of his apartment high-rise. He first does single steps to the top, descends, runs up the flight, descends, then he takes the steps two at a time and comes down. Set done. He does ten of these for a good aerobic workout. But there’s a reason why he varies his routine in one set, other than for mere variety. Being such a deep thinker, especially when doing rote exercises, he tends to forget mundane things, like how many repetitions he’s done. In fact, he is so deep, he can’t remember past one. If he did the same single-step climbs twice in a row, he would actually lose track of how many he did! What a brilliant guy! But this problem also applies to how many sets he’s done. To help him keep track, when he finishes a set, he can place little white stones (all identical) on a knee-high brick wall surrounding a well landscaped garden near the steps, thus keeping count.

Question: What is the least number of stones Bob needs to put on the brick wall to keep count in a ten-set workout? Explain.

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