Aug 28 2008
Mathematics Challenges
Below you will find a growing number of problems to solve.
You can do as many as you like, but should try at least one each week.
For each problem use this link to take you to a form where you enter your name and your answer. Each Monday we will compare answers and share strategies – if time permits.
(1) “The Builder”
To prepare a quote for some work on a block of land in the city, a builder asked the owner for the dimensions of the land.
“I can’t remember,” said the owner. “It’s shaped like a rectangle, ad I know that they needed ninety metres of fencing to enclose it. Oh, yes! The workers putting up the fence remarked that the lot is exactly twice as long as it is wide.”
“Thank you,” said the builder. “That’s all the information I need.”
How did the builder know the dimensions? Can you find the length and width of the lot?
(2) “The Book”
The pages of a certain book are numbered consecutively from 1 to 300.
How many page numbers contain the digit 5 and are also divisible by 5?
(3) “The Clever Milkman”
A milkman has only a 5 litre jug and a 3 litre jug to measure out milk for his cutomers from a milk churn.
How can he measure 1 litre without wasting any milk?
(4) “Sharing Marbles”
A bag of marbles can be divided in equal shares among 2, 3, 4, 5 or 6 children with no marbles left over.
What is the smallest number of marbles that could be in the bag?
(5) “Boxes of Marbles”
A company packages marbles in two different box sizes. One size holds 5 marbles and the other size holds 12 marbles.
The manager wants to package 99 marbles into more than 10 boxes, how many boxes of each size will there be?
(6) “The Town Hall Clock”
The clock in the Town Hall strikes 1 chime at 1 o’clock, 2 chimes and 2 o’clock, 3 chimes at 3 o’clock and so on.
How many chimes, in total, will the clock strike in a twelve-hour period?
(7) “Spending Money”
A woman spent thwo-thirds of her money. She lost two-thirds of the remainder and then had $4 left.
How much money did she start with?
(8) “Rectangles”
The perimeter of a rectangle is 22 centimetres, and each side of it is a whole number of centimetres.
How many different areas in square centimetres can the rectangle have?
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The answer to question 3″the clever milkman” is only fill up the 3 liter jug one thirds full.
The builder is width 15 on both sides and length 30 on both sides
the answer to “The Book” is 12 numbers
the answer to “boxes of Marbles” is 11 boxes. 7 big boxes and 4 small
question 2 is 36 fives in 300
5: 7 boxes with 12 marbles and 3 boxes with 5 marbles
The Builder answer is 15 width on both sides and 30 length top and bottom = 90
number 2 is 30
The Builder answer is 15 width on both sides and 30 length top and bottom equals 90