Problem Of The Week

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Problem Of The Week

• Edited by J. S.
• And animated by J. S.

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6 Problem of the Week
Little Billy was out trick-or-treating on
Halloween. He had gotten a lot of candy and was
peering into his bag, when out from behind a tree
came a mean goblin (actually it was his older
brother, Donald). The goblin reached into Billys
bag and took half of his candy plus one piece.
Within a few steps, Billy encountered a nasty
ghoul (actually it was his next-door neighbor,
Walter) who reached into Billys sack and took
half of his remaining candy plus two pieces.
Before he could turn and run, a scary ghost
(actually it was Tracy, the girl who sat behind
him in school) took half the candy that was left
plus three pieces. Now Little Billy began to cry
because he only had five pieces of candy
left. How many pieces of candy did he have before
Donald, Walter and Tracy raided his sack
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7 Problem of the Week
7 Problem of the Week The design below grows
each day as shown. If it continues to grow like
this, how many tiles will there be in the design
on the tenth day? On the fiftieth day? On the
ninth day? Day 1 Day 2
Day 3
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8 Problem of the Week
I snap my fingers now. In one second, I snap them
again. I wait two seconds and snap them a third
time. I wait four seconds before snapping them
again. Then I wait eight seconds, then sixteen,
and the pattern continues on. The interval
between snaps doubles each time. How many times
will I snap my fingers during the next year?
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9 Problem of the Week
Amys project in a metal shop class is to make a
box (with no lid). Her shop teacher gave her a
piece of metal that is 28 cm long and 20 cm wide.
The assignment is to form the box by cutting
squares out of each corner and bending the sides
up as shown below. The shop teacher, Mr. Rust,
will give extra credit to any student who forms
the box that holds the most when the cut-out
square is a whole number of centimeters on each
side. Amy wants the extra points! How large a
square should she cut from each corner to form
the box with the greatest volume?
28 cm
20 cm
?? cm
?? cm
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10 Problem of the Week
Each week our schools teams travel to other
schools for competitions. Today the five members
of the gymnastics team and seven weight lifters
are on their way to our rival school for meets.
The coaches would like the athletes on the two
teams to get to know one another, so they will
assign them to ride together in two vans. In how
many ways can five gymnasts and seven weight
lifters ride in two vans if no van contains more
than eight passengers and there is at least one
member of each team in each van?
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11 Problem of the Week
The design below grows each day, as shown. If it
continues to grow like this, how many tiles will
there be in the design on the tenth day? On the
fiftieth day? On the nth day?
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12 Problem of the Week

• Kenny and Tyler went apple picking. When their
  mother asked them how many apples they picked,
  they answered her with these clues
• If the apples were counted by twos, threes or
  fives, there would be one apple left over each
  time.
• If the apples were counted by sevens, there
  would be nothing left over.
• What is the smallest number of apples they could
  have picked?

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13 Problem of the Week
At a committee meeting, ten people were seated
around a circular table. At the conclusion of
the meeting, each person shook hands with
everyone else at the meeting except the people
who sat either to the right or to the left. How
many handshakes took place?
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