fawn nguyen: Puzzles and Brainteasers, Set 5

teaching math in middle school
learning from three teenagers
picking up dog poo

Puzzles and Brainteasers, Set 5

I love math.

Is 0 an even number? This question came up last week in my algebra class. One student immediately said, "No. It's neither." I then asked, "Why not?" So the kids went back and forth, and when they didn't hear from me, they asked, "Mrs. Nguyen, do you know the answer?" I rolled my eyes, "Of course I know the answer!"

I think I know. Zero should be even because math follows a pattern, and if I start with an even number, say 922, and count down by two's (and hopefully the period will be over), then eventually I get to 0, so it must be even.

In his book, A Passion for Mathematics, Clifford A. Pickover explains it much more eloquently:

Is 0 an even number? Yes. An even number leaves no remainder when divided by 2. So, 0/2 = 0 and has no remainder. Also, an integer n is called "even" if there exists an integer m such that n = 2m, and n is called "odd" if n + 1 is even. Thus, 0 is even by this criterion as well.

C'mon, I knew that. This question is from the same book.

Mystery Sequence

What rule am I using to determine the numbers in this sequence?

18, 20, 24, 30, 32, 38, 42, ...

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Someone has suggested that calling the equation "Distance = Rate x Time" the DIRT equation will help kids remember how to use it. My algebra kids have a tough time with DIRT and mixture problems, and they come up early in the school year. But to challenge the ones who do understand the basic problems in the textbook, I gave them this question.

Bus Stop

When Two buses leave at the same time from two towns — Salem and Morgan — on the same long road, traveling towards each other.

At each mile along the road are milestones. The buses' speeds are constant and in the ratio 5 to 4; the one leaving Salem is faster. The buses travel to and fro between the towns. They meet for the second time at the 145th milestone and for the third time at the 201st milestone. What milestones are at Salem and Morgan?

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I give out this PS every year to my geometry students.

Crawling Distance

A fly and spider are in a 12-foot high room having a 12-foot by 30-foot floor. The spider is on the 12 x 12 wall halfway between the adjacent walls and 1 foot from the floor. The fly is on the opposite 12 x 12 wall halfway between the adjacent walls and 1 foot from the ceiling. The spider wishes to crawl to where the fly is via the shortest possible route. How far will the spider travel?