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Friday, January 11, 2008

Rare Flowers

It was a day of special joy for Mrs. Greenhouse. She was exhibiting her collection of rare flowering plants to members of her garden club.
"Now these are my real treasures," she said in her best lecture voice, pointing to three luxuriously flowering specimens. "I got them from Guatemala only a year ago, and I have been giving them my closest attention. They are all quite delicate indeed. Since the flowers last only a single day. The plant with crimson flowers blossoms every fourth day, but I have to wait until the seventh day for the plant with lavender flowers. But that one is the most precious of all," she said, directing attention to her third plant."It takes a full thirteen days for it to blossom."
Since her three tropical flowering plants were such an enormous attraction, Mrs. Greenhouse expansively invited the club members to return to see them again."Let's make it next year on this very same day," she announced, "since they will all be in blossom them."
Was Mrs. Greenhouse correct in her horticultural reckoning?



SOLUTION :

If the club members come a year later on the very same day of the month, they would be one day later for the triple blooming. On the other hand, if they come next year on the very same day of the week(and as nearly as possible a year later), they would be right on time.
The least common multiple of 4, 7, and 13 is the smallest number divisible by all three numbers. Since this number is 4x7x13=364, it can be seen that the three plants blossom simultaneously every 364 days-52 weeks, but one day less than a full year. -Q.E.D-

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