[The Problem of the Week] quit! With the entry of the new smoking ban, perhaps few others can inspire the next problem to quit smoking:
Ms. Menchu, a heavy smoker for many years, finally decided to quit upon learning of the malignancy of snuff and see all her friends were leaving now. "I will end the 27 remaining cigarettes," he said, "and never smoke again."
The habit of smoking Ms. Menchu \u200b\u200bwas exactly 2 / 3 of each cigarette.
Before long discovered that with the help of adhesive tape could hit three cigarette butts and do another.
With 27 cigarettes, how many smoking snuff before leaving for good?
We
resolution below the image.
[John Norwood is an artist who has performed, among other works, geometric sculptures snuff packages. The image is taken from the artist's web
.]
Solution:
When the 27 smoke 27 cigarette butts are left, each 1 / 3 of cigarettes. Is obtained by joining three cigarette butts, then with the 27 butts Menchu \u200b\u200b9 cigarettes can make more. But here are just the thing when you smoke these 9 cigarette butts you have 9, and 3 cigarettes they can develop more, and when you smoke these, with the 3 remaining butts can get a last cigarette, which will give a last butt, and is itself no longer can use.
Total: 27 + 9 + 3 + 1 = 40 cigarettes in total.
Enlargement:
We've added a small geometrical progression four terms, with initial term 27 and right 1 / 3. If we allow Menchu \u200b\u200bcontinue smoking the cigarette he had left and it continues to meet every time the size of the cigarette is reduced by 2 / 3, we could continue the sum of the progression
27 + 9 + 3 + 1 + 1 / 3 + 1 / 9 + 1 / 27 + ...
This infinite progression is a finite sum, calculated with the operation 27 / (1 - 1 / 3) = 81 / 2 = 40.5
Note: This problem is quite old and I think it is the first I propose instead that the apprentices as a problem of the week. By the way, never too late to remember and insist that snuff smoking is injurious to health , And in each breath we are introducing into the body thousands of poisonous substances that eventually we can produce all kinds of diseases, especially cancer. I hope nobody is taking this problem occurs, or the image contained in it as an inducement to smoking.
