94-Math Riddles 01

Today we will see some riddles. Actually, the riddles are very simple. Only we need to think about the riddle with the basic concept of the topic.

We all know the decimal system very well. There are 10 digits say 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. In this riddle, we changed all the values of digits 0 to 9. On the basis of these changed values of all these digits, the following problems are solved. Study all these problems very carefully.

Let us discuss some steps of the solution to such problems.

Solved Example:

Key-1

      The Sum of all the digits from 0 to 9 is 58.

Key-2

     853
  + 388
-----------
     818

Key-3

     5381
  + 1573
-------------
    26501

Key-4

     9
  x 6
-----------
   75

Step-1

Using Key 1:

As we know that the sum of all the digits from 0 to 9 is 45 in the actual case. Here is the problem, for changed values of the digits, the sum is 58 so the original digit for 5 is 4 and that of 8 is 5. This means, for a new value of 5, the original value of the digit is 4 and for a new value of 8, the original value of the digit is 5.

Step-2

Prepare a chart of New values and the original values of all the digits as shown below:

Original Digits	0	1	2	3	4	5	6	7	8	9
New Values of Digits					5	8

Like this, find out all the values of the remaining digits from other keys given in the question.

Using Key 2:

Problem with new values          Problem with original values

      853                                            54a             540                            
   + 388                                         + a55          + 055
  ---------                                          ----------         ----------
      818                                           5b5             595

Here, a + 5 = 5, a = 0, so, 3 is 0 and here we have to add 540 and 055 which comes to 595 so b = 9 i.e. 1 is 9.

Now write the original values of 3 as 0 and 1 as 9 in the following table.

Original Digits	0	1	2	3	4	5	6	7	8	9
New Values of Digits	3				5	8				1

Using Key 3: From the above table, we have,

Problem with new values          Problem with original values

      5381                                       4059                4059                            
   + 1573                                    + 94a0             + 9420
  ------------                                     ----------            ----------
     26501                                     dc4b9              13479

Here, it is clear that d = 1 and c = 3 as 4 + 9 = 13 with no carry from the previous digits. Secondly, a can't be 6, 7, or 8 as no carry is forwarded. So a must be 2, i. e. 7 is 2. As 5 + 2 = 7, where b is 7, i. e. 0 is 7.

Now write the original values of 7 as 2, 0 as 7, 2 as 1, and 6 as 3 in the following table.

Original Digits	0	1	2	3	4	5	6	7	8	9
New Values of Digits	3	2	7	6	5	8		0		1

Using Key 4: From the above table, we have,

Problem with new values          Problem with original values

      9                                       a                     8                          
   x 6                                    x 3                   x 3
 -------                                 ----------            ----------
    75                                     24                   24

Here, it is clear that a = 8 as 8 x 3 = 24. So a must be 8, i. e. 9 is 8, and the remaining 4 must be 6.

Now write the original values of 9 as 8, and 4 as 6 in the following table.

Original Digits	0	1	2	3	4	5	6	7	8	9
New Values of Digits	3	2	7	6	5	8	4	0	9	1

Now we can answer all the questions if the new value is allotted to any digit.

Using the above-solved example, we can answer the following:

1) Using the following keys, answer the questions asked below these keys:

Key-1

      The Sum of all the digits from 0 to 9 is 80.

Key-2

     801
  + 488
-----------
    7248

Key-3

     086
  + 167
-----------
     954

Now answer the following?
a) What is the new value of 3?
b) Write the product 245 x 359 with the answer in new values.
c) Find the original value of 375.
d) Re-write the "(809+548)/70" in original values.

Anil Satpute