Brilliant Garden
Calvin has cut a flower from the Brilliant Garden, and when he pulls out every petal he says: "I love math:
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a little (first petal),
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too much (second petal),
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passionately (third petal),
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with madness (fourth petal),
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nothing (fifth petal),
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a little (sixth petal),
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too much (seventh petal), ... "
The flower of the Brilliant Garden is an extraordinary flower. When it is extracted from the plant, it has 95 petals, but the most incredible thing is that, after pulling out 5 petals, it instantly grows a new one.
When Calvin ripped off the last petal of the flower, how many petals did he take off in all?
Bonus:
When the last petal was removed, what did Calvin say?
The answer is 118.
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1 solution
Take off the initial 95 petals. As you take off the 95th, the 19th regrown petal sprouts.
Take off 15 more (total = 110): 3 new petals will have grown, leaving the flower with (19 - 15 + 3) = 7 petals.
Take off 5 more, leaving 2, and a 3rd petal sprouts. At this stage you have removed 115 petals. Take off the final 3, and you have removed 118.
Since the cycle of what Calvin says repeats modulo 5, what he says after removing the 118th petal is the same as what he says after removing the 3rd petal. "Passionately."