http://webmaths.wordpress.com/2010/08/06/thirty-numbers/
(Though I saw the puzzle back when it first appeared, I've never seen the solution, so hopefully a reader may be able to provide it! -- not even sure if it requires some involved math, or has, as I suspect, a simple, easily-overlooked solution):
"I have a list of thirty numbers where the first number is 1, the last number is 30, and each of the other numbers is one more than the average of its two neighbours. What is the largest number in the list? "(One thing I'm not clear on: from the problem as stated, I don't know if the 30 listed numbers must be distinct, different integers, or may include numbers that repeat themselves.)
4 comments:
using Excel an iterative method the numbers i get are 1, 30, 57, 82, 105, 126, 145, 162, 177, 190, 201, 210, 217, 222, 225, 226, 225, 222, 217, 210, 201, 190, 177, 162, 145, 126, 105, 82, 57, 30. which means the largest number in the list is 226.
Thanks James for that answer, though it seems a bit brute force; the problem was given to "Intermediate (year 9 and 10)" students so I can't help but believe there is a simpler answer??? Anyone else got a thought...
apparently yahoo answer had an answer http://answers.yahoo.com/question/index;_ylt=An3o8R4WZ8AcGUvXVn0z8e4jzKIX;_ylv=3?qid=20100806223624AAGwZBw
THANKS again James! very interesting; I wonder how many of the Australian students got the right answer???
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