clix - Lessson 1: Making and Solving Puzzles

Activity 3: Guess the Number

Another set of puzzles can be created by using simple numbers. Let us take any number, say 65.

We can represent 65 in a variety of ways.

65 = 60 + 5
65 = 12 × 5 + 5
65 = 14 × 5 - 5
65 = 8 × 10 - 5 × 3
65 = 10 × 5 + 3 × 5
65 = 50 + 15
The puzzle can be set like this:

If we remove 5 from this number, the result is 5 times 12. What is the number?

Let’s try to find the answer.
Let the number be n.
The information we have been given is that
n − 5 = 5 x 12 = 60
or

n − 5 = 60
n = 60 + 5 = 65, which is the number we are looking for.

Here is another example of a puzzle set around the number 65:

We have seen that 65 can be represented as

50 +15.

That is, 65 = 50 +15

This means

65 − 15 = 50
Here’s the puzzle.
If you remove three times a number from 65, you will get 10 times that number. Can you guess what the number is?

Let n be the required number. Then, three times the number is 3n; and ten times the number is 10n.

We can write this as:
65 − 3n = 10n
Which is
65 = 3n + 10n
or

65 = 13n Hence the required number, n = 5
We will now use a tool which will help us to write a number in different ways. Let us see how this is done.

Type a number which you want to factorize. From the ten buttons, you can click on any of the ten buttons (each button having a number from 1 to 10), which will m factorizeng our number by the number on the button. This way, we can see how a number can be written in various ways.
To clear the screen, click on “Erase” button.

factorise_1

Now, try it yourself

Lets solve some puzzles nowWe will solve a few number puzzles:
Question 1:
When you subtract it by 5, it becomes 2 times four. Guess the number

Question 2:
Guess the number which, when divided by 5, gives a number that is 5 less than 70.

Using the Number Tool Puzzle-Maker, you can create puzzles based on numbers. First, solve the puzzles yourself. Then, post them for your friends in the Comment box below.

Then, invite your friends to post puzzles of their own. You can post your answers by clicking on the Reply button below the comments.

You will also be able to check if your friends have posted their answers to the puzzles you set.