Even doordenken! Wiskundepuzzels.

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

Even doordenken!

For a change and for getting a little more flexible in your Maths skills, you are going to solve a number of 

Math Puzzles!   

18 Math Puzzles will come your way ...

+ simple 

+ tricky

+ even difficult, but all ..

+ worth while thinking over!

+ in Pairs or on your own.

after a while you may ...

+  read out a Puzzle to your own choice to the class, and

+  show the way how you found the Solution!

+ First let's look at a few examples.

+ In English, although all Puzzles are in dutch.

Example 1:

The three of us eat a pie.

A eats      ,  B   eats        and C eats the rest.

How much did C get?

​4​​1​​

​8​​5​​

​8​​7​​

​8​​1​​

How much did C get?
(Explanation next slide.)

1. 1/7
2. 1/4
3. 1/3
4. 1/8

Example 1:

The 3 of us eat a pie. We are A, B and C. 

A eats      ,  B eats        and C eats the rest.

T solve this, we have to add up the following fractions:         and  

      +        =   

So for C there is         left.  Because  1 =               and        -          =   

​4​​1​​

​8​​5​​

​8​​7​​

​8​​1​​

​4​​1​​

​8​​5​​

​8​​2​​

​8​​5​​

​8​​7​​

​8​​1​​

​8​​8​​

​8​​8​​

​8​​7​​

Example 2:

Warning: this one is more difficult. However, maybe you find a way to tackle it?!

Three friends, Amy, Brenda and Cathy, win a price in the Lottery.

They divide it up as follows:

1.    Amy gets three times as much as Brenda

2.   Cathy gets two times as much as Amy.

3.   Together they divide up 40 euros.

QUESTION: How much do Amy, Brenda and Cathy get?

How much does Cathy get?

1. 16 euros
2. 24 euros
3. 12 euros
4. 4 euros

Explanation:

A new method is introduced here. Just try and follow this. (Maybe you can use it to solve a few of the Math Puzzles!)

They divide it up as follows:

1.  Amy gets three times as much as Brenda

2. Cathy gets two times as much as Amy.

3. Together they divide up 40 euros.

Solution: the key step is the first:

a. Let's call the part Brenda gets:   h                   (This may seem mysterious to you but it turns out to be very helpful!)

b. Then Amy gets 3 x h     and    Cathy gets 2   x   3 x h = 6 x a. 

Example 2 - follow up

Solution: the key step is the first:

a. Let's call the part Brenda gets:   a                   (This may seem mysterious to you but it turns out to be very helpful!)

b. Then Amy gets 3 x a     and    Cathy gets 2   x   3 x a = 6 x a. 

Now we add up the parts the 3 girls get:     a + 3 x a + 6 x a = 1 x a + 3 x a + 6 x a = 10 x a 

So   10 x a = 40 euros, because 40 euros is what they may divide up.

Then a = 40 euros : 10 = 4 euros.

ANSWER: Brenda gets 1 x a  = 1 x 4 euros = 4 euros                Amy gets 3 x a = 3 x 4 euros = 12 euros   and finally

Cathy gets   6 x a = 6 x 4 euros = 24 euros.    Check:    4 + 12 + 24 = 40 euros.              Checks out all right.

Maybe this last example was pretty difficult for you.

+ That's only logical as a complete new Math technique was used here!

+ However, not all Puzzles are that complicated.

+ Some are even very easy.

+ Some have more to do with Language than with Maths.

+ So there is something for everyone! (See next slide.)

MCMLXX is a Roman number

What year does it mean in our number system?

A little help:

M = 1000        C = 100      L = 50     X = 10

SOLUTION:

MCMLXX is a Roman number.

It means:                1970.  How to find that out?

M = 1000,        C = 100,         L = 50       and       X = 10

Rules for Roman numbers:

If a lower number preceeds (voorafgaan) aan a higher one then it is subtracted.

So we get:  1000 - 100 + 1000 + 50 + 10 + 10 =  1970

Solve a few Math Puzzles now!

Have fun!

+  Note: the Puzzles are not connected in any way.

+ That's why you may choose which one you do first.

+  Do this with a neighbour or on your own.

+  You don't have to finish them all. Better do a few good!

+  Write down your answers on the paper I'll give you.

In 4 minutes time I ask some of you to explain one of the Puzzles.

Time to explain a few Puzzles to the class!

Try to solve a few more Puzzles.

What is your opinion of this lesson?