LINEAR EQUATIONS

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

A puzzle for the statement 65 = 12 × 5 + 5 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.
or, n = 60 + 5 = 65, which is the number we are looking for.

Here is another example of a puzzle set around the statement 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.
or, 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 many different ways. Let us see how this is done in the GIF below:

Type a number which you want to factorize. From the ten numbered buttons, you can click on any of them with which our number will get factorized. This way, we can see how a number can be written in various ways. To clear the screen at any stage, click on the “Erase” button.
 

Replay Animation

Now, try it yourself:
 

Let us solve some number based puzzles now.

Puzzle 1:  When you subtract a number by 5, it becomes 2 times four. Guess the number.

Puzzle 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. After making the puzzles, first, solve them 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.