1. MATHEMATICS PUZZLES
Circling The Square Puzzle
The Puzzle:
In the diagram below, each circle is just big enough to touch all four sides of the
square. The area of the square is therefore just a bit more than the area of one
of the circles.
I want to know how many of the circles you need to cover the whole square. Is
2 enough? Or do you need 3? Or 4? Or more?
I have put 5 circles for you to play with (print and then cut them out), but what
is the least number you need?
2. Our Solution:
The actual answer is that you need FOUR circles to cover the square completely.
But because it is so difficult to cut out the circles accurately enough to see the
tiny gaps that appear, you can be happy if you answered three circles. But four
is correct, and you can actually use a program like "GeoGebra" to solve it.
3. Cut a 3x3 Cube Puzzle
The Puzzle:
Imagine a 3x3x3 cube.
How many cuts do we need to break it into 27 1x1x1 cubes?
A cut may go through multiple pieces.
Our Solution:
The central 1x1x1 cube has six faces.
Any cut can only reveal one of these faces!
So six cuts are needed, and also are enough.
4. Matches Of The Day Puzzle
The Puzzle:
The diagram shows 3 squares and 2 triangles.
Rearrange the matches to make 5 squares and 6 triangles.
Our Solution:
Note that there are four small squares and four small triangles. Can you also
see the large square and the two large triangles?
5. Ten Balls in Five Lines Puzzle
The Puzzle:
Place 10 balls in 5 lines in such a way that each line has exactly 4 balls on it.
Our Solution:
6. Parted Circle Puzzle
The Puzzle:
You have nine circles (divided into 16 smaller sectors). Each has a different
pattern of holes. Which two of them can form an opaque (non-transparent)
circle when stacked on top of each other?
Circles can be rotated and/or overturned.
8. 5-digit Number Puzzle
The Puzzle:
What 5-digit number has the following features:
If we put the numeral 1 at the beginning, we get a number three times smaller
than if we put the numeral 1 at the end of the number.
Our Solution:
We can make an equation:
3(100000 + x) = 10x+1
(Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and
multiplying by 10 and adding 1 puts a 1 at the end of a number)
Solving this gives:
10x+1 = 3(100000 + x)
10x+1 = 300000 + 3x
10x = 299999 + 3x
7x = 299999
x = 299999/7 = 42857
The answer is 42857 (142857 is three times smaller than 428571)
9. A Unique Number Puzzle
The Puzzle:
What is unique about 8549176320 ?
Our Solution:
It is the digits 0 to 9 in alphabetical order.
10. Missing Number 1 Puzzle
The Puzzle:
What is the missing number in Triangle Four?
Our Solution:
The product of the two largest
minus the square of the smallest,
So the missing number is 45-16 = 29
11. Broken Stick Puzzle
The Puzzle:
A 1-metre stick is broken into two pieces at random. What is the length of the
shorter piece, on averag
Our Solution:
The shorter piece will be randomly from 0cm to 50cm long, with an average of
25cm
12. Clock in the Mirror Puzzle
The Puzzle:
Joey leaves his house in the morning to go to day camp.
Just as he is leaving his house he looks at an analog clock reflected in the
mirror.
There are no numbers on the clock, so Joey makes an error in reading the time
since it is a mirror image. Joey assumes there is something wrong with the
clock and rides his bike to day camp.
He gets there in 20 minutes and finds that just as he gets there the day camp
clock has a time that is 2 1/2 hours (2 hours and 30 minutes) later than the
time that he saw in the mirror image of his clock at home.
What time was it when he got to day camp?
(The clock at camp and the clock at home were both set to the correct time.)
Our Solution:
First subtract 20 minutes from 2 1/2 hours to compensate for his 20 minute
bike ride to give a difference of 2 hours and 10 minutes.
To be a "Mirror Effect" it must be mirrored around 12 o'clock (when the hands
are straight up), or around 6 o'clock (when the hands are pointing up and
down), as we know he left in the morning, it must be 6 o'clock.
So, divide that 2 hours and 10 minutes by 2 and this will give you the center-point
(65 minutes) for compensating for the mirror.
By adding that 65 minutes to 6 o'clock you get the time he left home (7:05),
and the time he saw in the mirror (4:55).
Furthermore, by re-adding the 20 minutes from when he left (7:05), you get
what time he got to camp (7:25).
