notes
Letters for Digit:
Here we have puzzles in which letters take the place of digits in an arithmetic ‘sum’, and the problem is to find out which letter represents which digit; so it is like cracking a code. Here we stick to problems of addition and multiplication.
Here are two rules we follow while doing such puzzles.
- Each letter in the puzzle must stand for just one digit. Each digit must be represented by just one letter.
- The first digit of a number cannot be zero. Thus, we write the number “fifty-three” as 53, and not as 053, or 0053.
1) Puzzles with addition:
1) Find Q in the addition.
Solution:
There is just one letter Q whose value we have to find.
Study the addition in the one's column: from Q + 3, we get ‘1’, that is, a number whose one's digit is 1.
For this to happen, the digit Q should be 8. So the puzzle can be solved as shown below.
That is, Q = 8
2) Puzzles with multiplication:
Find the value of A and B in the below multiplication.
B × 7 = B, it is possible if B = 0 or B = 5
If A = 1 and B = 0, AB × A7 = 10 × 17 = 170
If A = 1 and B = 5, AB × A7 = 15 × 17 = 255
If A = 2 and B = 0, AB × A7 = 20 × 27 = 540
If A = 2 and B= 5, AB × A7 = 25 × 27 = 675
If A = 3 and B= 0, AB × A7 = 30 × 37 = 1110
If A = 3 and B = 5, AB × A7 = 35 × 37 = 1295
Example
Find A and B in the addition.
A | |
+ | A |
+ | A |
B | A |
The sum of three A’s is a number whose one's digit is A.
The sum of two A’s must be a number whose one's digit is 0.
This happens only for A = 0 and A = 5.
If A = 0, then the sum is 0 + 0 + 0 = 0, which makes B = 0 too.
We do not want this, so we reject this possibility.
So, A = 5.
Therefore, the puzzle is solved as shown below.
5 | |
+ | 5 |
+ | 5 |
1 | 5 |
That is, A = 5 and B = 1.
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