Page 74 - Ganit Kaushal

Ex 1. Mark the supercells in the table below. (NCERT)

6828 670 9435 3780 3708 7308 8000 5583 52

Sol. The coloured cells in the following table are supercells.
The leftmost cell is a supercell because 6828 is larger than 670.
The 3rd cell from the left is a supercell because 9435 is larger than 670 and 3780 both.
The 3rd cell from the right is a supercell because 8000 is larger than 7308 and 5583.

6828 670 9435 3780 3708 7308 8000 5583 52
Ex 2. Fill in the table below with only 4-digit numbers such that the supercells are exactly the coloured cells.

5346 1258 9635 (NCERT)
Sol. There can be many solutions to this problem, depending upon the thinking of the reader. The table
below is one of those solutions which shows that the coloured cells are super cells.

5346 5400 1000 1258 1200 1150 2200 9635 9700
(Readers are advised to explore some more solutions to this problem.)
Now, let’s make this supercells game more interesting by increasing the number of rows. Here, the neighbouring
cells are those that are immediately to the left, right, top and bottom.

The rule remains the same: a cell becomes a supercell if the number in it is greater than all the numbers in its
neighbouring cells.
For example: In Table-1, 8631 is greater than all its neighbours 4579, 2331 7500 7350 9870
8280, 4795 and 1944. So, it is a supercell and is coloured green. Similarly,
7500 is greater than its neighbouring cells 2331, 4795 and 7350. So, 3115 4795 9124 9230
it is a supercell. 9870 is a supercell because it is larger than its two 4579 8631 8280 3446
neighbouring cells, 7350 and 9230. 6034 is a supercell, as it is larger than 5785 1944 5805 6034
3446 and 5805. Similarly, 5785 is a supercell as it is larger than two of Table-1
its neighbouring cells 4579 and 1944.

There is a total of five supercells, all coloured green.
Can we have two consecutive supercells in a row or in a column?
Excellent, you’re right again. The answer is a big No. We cannot have consecutive supercells in a row
or a column. The reason for this is simple two numbers cannot be larger than each other at the same
time, and a supercell has to be larger than its adjacent cells in that row and column.
Can we have two consecutive supercells diagonally?

Excellent, you’re right again. The answer is Yes! Observe table-1 given above.
Readers are advised to make some more such tables and fill them with numbers so that they can have the
maximum possible supercells.

Interchanging the Digits

Now, let us see the effect of interchanging two digits in a supercell table. Observe in table-1: the supercell
8631 will not remain a supercell if we interchange 8 and 1, and the number 9124 will become a supercell if we
interchange 1 and 4. So, the number of supercells can be increased or decreased by interchanging two digits
in the cells. Let’s have an interesting example.

72 Mathematics-6