Math Problems of the
Month
OSU-Marion
April 2005
Try your hand at these problems. Each Month I will post a few of my
favorite math problems and puzzles. Some can be solved by algebra, some
need some clever intuition, some need a little elbow grease. I hope you enjoy
them as much as I do.
Submit answers to Dr. Maharry in MR 370 or at
maharry@math.ohio-state.edu.
I will post the names of those who submit correct solutions
outside my door and on my web site.
- A woman starts out with a certain amount of quarters. She
gives one fifth of the amount plus four more to her daughter. Then she gives
one fourth of the remaining quarters plus three more to her son. Next she
gives one third of what’s left plus four more to her grandson, and finally one
half of what remains plus five more to her granddaughter. After all of this,
she is left with 10 quarters. How many did she start with? Who ended up with
the most quarters?
- Suppose you work in a hotel and down one hall way you
have rooms numbered 1 through 100. All the doors are initially closed. Out of
boredom, you make 100 trips down the hall passing by all the doors starting
with the room #1 every time. The first time down the hall you visit every door
and open the door if it was closed and close it if it was open. (Why do you do
this?, I have no idea.) The second time down the hall you only visit every 2nd
door (door #2, #4, #6) and either and open the door if it was closed or close
it if it was open. The third time down the hall you switch every 3rd door
(door #3, #6, #9). Repeat this 100 times down the hallway.
Question: what state are the doors in after the last pass? Which doors are
open which are closed? Can you figure it out without actually making 100
passes? Look for a pattern.
- Draw a square. Divide it into four identical squares.
Remove the bottom left hand square. Now divide the resulting shape into four
identical shapes.
- Mr. and Mrs. Adams recently attended a party at which
there were three other couples. Various handshakes took place. No one shook
hands with his or her own spouse, no one shook hands with the same person
twice and no one shook his or her own hand. After the handshaking was done,
Mr. Adams asked each person, including his own wife, how many hands they had
shaken. Each gave a different answer. How many hands did Mrs. Adams shake?