Page 85 - Math_Genius_V1.0_C6_Flipbook
P. 85
E:\Working\Focus_Learning\Math_Genius-6\Open_Files\04_Chapter_3\Chapter_3
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________
Shifting of Digits
Do you know what happens when two digits in a number are interchanged?
Let us consider the number 7253. Observe the following:
Observation
Interchanging 7 with 3, we get 3257 7253 > 3257
Interchanging 7 with 5, we get 5273 7253 > 5273
Interchanging 2 with 3, we get 7352 7253 < 7352
Interchanging 2 with 5, we get 7523 7253 < 7523
Take some other numbers and try this.
Example 7: There is only one supercell (a number greater than all its neighbours) in this grid.
If you interchange two digits of one of the numbers, there will be 4 supercells. Figure out which
digits to swap.
16,200 39,344 29,765
23,609 62,871 45,306
19,381 50,319 38,408
Solution: If we swap the digits, 6 and 1 of 62,871, we get the 4 supercells as shown in the table.
16,200 39,344 29,765
23,609 12,876 45,306
19,381 50,319 38,408
Quick Check
1. Make the smallest and the largest 4-digit numbers using the digits 2, 5, 9, and 1. Find the sum and
difference of the numbers so formed. Are they also 4-digit numbers?
2. There is only one supercell in this grid. If you interchange two digits of 36,200 39,344 20,765
one of the numbers, there will be 4 supercells. Figure out which digits 63,609 82,675 54,306
to swap. 49,381 50,319 37,084
Palindromic Pattern
Look at the following words: MOM, DAD, NOON, MADAM.
Look at the following numbers: 12321, 3547453, 1331.
Look at the date: 22/02/2022.
These words, numbers and date are same when read from left to right or vice versa.
In the 8th century, a mathematician named Mahavira in his book Ganita Sara Sangraha, discussed
about Garland numbers/Palindrome numbers.
To find a palindrome number, follow the steps given below.
Take a number and reverse it. Add the original number with the reversed number obtained. Check
if you get a palindrome number. If not, repeat the process.
83 Number Play
