Playing with Numbers

General form of numbers

We all are familiar with puzzles in books, magazines, newspapers etc. Here, we introduce a new type of puzzle where you will need to find some missing numbers using the basic properties of mathematics.

Let us look at the following puzzle.

How can we find the missing numbers?

In the first column, the sum of 7 and another digit cannot be 2, as 2 is less than 7. Hence, it is logical that the number may be 12 as.

Thus, in the first column the missing number is 5.

The second column has a carryover value of 1.

Thus, it becomes

Now, it is clear that the missing number is 3.

Therefore, we can write

We can also write the same problem as

Finding the missing values in the previous example is the same as finding the values of letters in the given problem.

Here, the digits are denoted by the letters of the English alphabet and only one digit is denoted by one letter.

For example, let us try to find the value of A in the following example.

Here, we add a digit three times and get the same digit at the units place.

Such digits are 0 and 5.

If we take A as 0, then the addition of three 0s equals 0. However, we cannot get any number in the tens place. In the problem, we can see that the sum has 1 in its tens place. Let us now take the digit 5 as the value of A.

If A = 5, then

Therefore, the value of A is 5.

Let us discuss some more examples to better understand this concept.

**Example 1:**

**Find the values of the letters in the following puzzles:**

**Solution:**

**(i)** We have

Here, the sum of A and 2 is 6.

Thus, A is 4.

On replacing letter A with its valu…

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