Our school participates in a program called, Math Olympiad. Kids in 4th thru 6th grade are given monthly math tests (only 5 problems each time). It doesn't matter which grade you are, everyone gets the same test. The problems are really hard - see if you can solve this example:
Time Limit: 6 minutes
Bay Street has between 1 and 15 houses, numbered 1, 2, 3,
and so on. Mr. Sullivan lives in one of the houses. The sum
of all the house numbers less than his equals the sum of all
the house numbers greater than his. How many houses are
there on Bay Street?
Bay Street has between 1 and 15 houses, numbered 1, 2, 3,
and so on. Mr. Sullivan lives in one of the houses. The sum
of all the house numbers less than his equals the sum of all
the house numbers greater than his. How many houses are
there on Bay Street?
Did you get it? See the answer below.
Anyway, Brennen scored high enough to earn this patch. He was one out of five kids from the forth grade that earned a patch. Only THREE 5th graders & 12 6th graders earned a patch - which means, that Brennen was able to do better than most 4th, 5th & 6th graders. Remember, they all took the same test. Way to go Brennen! I can't wait to see what he does next year.
Here is your answer & solution:
Consider the first few houses on a street, then the house Mr. Sullivan might
live in, and then the first few houses that come after that.
Beginning of Street Mr. Sullivan End of Street
1 + 2 + 3 = 6 4 5 + 6 = 11 …… Too big
1 + 2 + 3 + 4 = 10 5 6 + 7 = 13 …… Too big
1 + 2 + 3 + 4 + 5 = 15 6 7 + 8 = 15 …… Equal sums
Therefore, there are 8 houses on Bay Street.
