Monday Math Madness #18: Winner!
07 Nov 2008 Quan Quach 7 comments 43 views
MMM #18 Winner
The winner for this edition of MMM is Troy Williams. Congratulations Troy on solving two nearly impossible math problems. This rendition of MMM was a little different and might have been a tad too easy as EVERYONE who submitted an answer got it correct! I’m sure that Sol will more than make up for this by posing an extra difficult problem over at wildaboutmath.com this coming Monday.
The two questions were apparently so easy that we even got a response from an 8th grader in Colorado. Honorable mention goes to Kathleen Braun! Thanks for participating, and thanks for showing me that young people are interested in math!
The Answer by Kathleen Braun
Part 1
If the ball is dropped from a height of 64 feet and bounces back half
the distance each time, the vertical distance is 64 feet to the floor
followed by a vertical distance up of 32 feet and a drop of 32 feet to
the floor,folled by 16 feet up and another 16 feet down before it has
hit the floor 3 times. The total vertical distance is, therefore, 64 +
32 + 32 +16 +16 = 160 vertical feet.
Part 2
The oranges are stacked in a pattern that can be described by
[N(N+10]/2 with N from 1 to 10 inclusive the sum of the oranges in the
first 10 stacks equals 220 oranges.
7 Responses to “Monday Math Madness #18: Winner!”
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ummm … can the equation [N(N+10]/2 be clarified? a right parenthesis is missing? and shouldn’t N=1 result in the equation equaling 1 since that’s how many oranges are on the top layer? Thnx
Good question. I’m hoping kathleen stops by to explain her answer
The expression [N(N+10]/2 should actually be [N(N+1)]/2. Kathleen likely forgot to hit the Shift key when typing the closing parentheses.
N*(N+1)/2 is the Nth triangular number:
http://en.wikipedia.org/wiki/Triangular_number
The fact that the total number of oranges in the pyramid is the sum of triangular numbers makes sense when you realize that layer N of the pyramid is a triangle with side N.
This page talks a little bit more about the relationship between triangular numbers and pyramid stacks:
http://en.wikipedia.org/wiki/Tetrahedral_number
The equation N*(N+1)/2 comes from the solution to the Summation of n from 1 to N. This just happens to be the pattern of triangles (or bowling pins).
Yes I believe Steve and Bob are correct. I was really hoping Kathleen would stop by though.
Kathleen was technically wrong as she gave her answer in feet… a little nitpicky, sure, but it would have been marked incorrect on any highschool or college quiz.
Also, I think classifying these problems as “nearly impossible” is quite a stretch. I was able to do both in my head minutes after reading them. I’m not bragging, I’m sure there are plenty of people that could of.
Thnx Steve and Bob. HAHAHAHA - I totally missed that shift+0 = ) … I was initially thinking [N(N+10]/2 was suppose to be [N(N+10)]/2 which I knew couldn’t be correct.
Poh, “nearly impossible”+”might have been a tad too easy as EVERYONE who submitted an answer got it correct!” = sarcasm! (that’s a factorial not exclamation mark)
Thnx again Steve and Bob