High School Math Page Archive: 2002
You can browse the selection of puzzles and problems below, or choose other options from the navigation bar to the right.
| Merry Christmas, Mr. Spencer!
An absentminded bank teller switches the dollars and cents
when he cashed a check for Mr. Spencer, giving him dollars instead of cents, and cents
instead of dollars. After buying a five cent newspaper, Mr. Spencer discovered he had
left exactly twice as much as his original check. What was the amount of the check?
view solution |
Dec 1, 2002 | If you square me, I'll square you!
"Give two different numbers, each of which is the square of the other."
view solution |
Nov 1, 2002 | The long walk
A few months ago, we had a running dog. This month it's a walking fly.
An elastic strip of length 1m is attached to a wall and the
back of a car. A fly starts at the wall and crawls on the strip towards the car, which
at the same time drives away from the wall at a speed of 1m/s.
Assuming that the strip can be stretched infinitely long, will the fly ever reach the
back of the car?
view solution |
Oct 1, 2002 | Have a Fibonacci Day!
Have a Fibonacci Day!The Fibonacci numbers are defined as F0 = F1 = 1 and Fn+1 = Fn + Fn-1.
Calculate the following infinite sum:
F0 3F1 32F2 3nFn
--- + ---- + ----- + ... + ----- + ...
1 5 52 5n
view solution |
Sep 1, 2002 | What is this geometric sequence?
The sum of the first few terms in a geometric progression is 11, the sum of their squares is 341, and sum of their cubes is 3641. Find the terms of the sequence.
view solution |
Aug 1, 2002 | Holey Sphere!
Suppose a circular hole was drilled through the center of a sphere. When the length of the hole was measured along its wall, it was found to be six inches long.
What is the volume of the part of the sphere that remains after the material is removed from the hole?
Express your answer as an exact real number number of cubic inches.
You don't need calculus to solve this problem (but if you know how to
do it using calculus, go ahead) as long as you know the volume of a sphere is
(4/3)π r³.
view solution |
Jul 1, 2002 | The Running Dog
"Yes, when I take my dog for a walk," said a mathematical friend, "he frequently supplies me with some interesting puzzle to solve. One day, for example, he waited, as I left the door, to see which way I should go, and when I started he raced along to the end of the road, immediately returning to me; again racing to the end of the road and again returning. He did this four times in all, at a uniform speed, and then ran at my side the remaining distance, which according to my paces measured 27 yards. I afterwards measured the distance from my door to the end of the road and found it to be 625 feet. Now, if I walk 4 miles per hour, what is the speed of my dog when racing to and fro?"
view solution |
May 6, 2002 |
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