mathematics

1. MATHEMATICAL GAMES
Times hitori……
1 2 3 6 6 8 2 9
1 4 3 5 6 9 2 8
8 8 2 8 9 1 2 3
5 5 4 8 3 5 7 9
2 3 2 7 2 4 9 6
1 9 1 4 2 8 3 5
5 1 3 2 6 6 5 7
9 6 8 3 1 7 5 4
How to play
(1) A number may repeat just once in each row
or column. Eliminate repeating number by
darkening cells.

2. (2) Darkened cells must never be adjacent in a row
or column.
(3) Unmarked cells must create a single continuous
area undivided by darkened cells.
(4)
Every time you darken a cell you
can automatically circle its vertical and
horizontal neighbours which
may cannot be eliminated.

3. Any cell ‘SEND WICHED’
between neighbours of
the some value can be
circled.
(5)

4. Example:
8 5 5 7 3 5 4 6
4 5 1 6 7 6 5 2
2 5 7 1 5 4 6 8
5 6 2 4 3 7 6 3
2 7 5 5 1 7 2 7
1 6 6 6 4 3 5 7
7 8 4 6 2 3 3 7
8 4 5 2 3 5 7 1
(6) A ‘triple’ is a special case of sand which circle
the centre cell and darken the ends. e.g. 666.

5. CARTOONS
Hello Mickey.
How are you?
I am fine Ben.
Mickey do you know
about real numbers?
Yes I know in class
Xth. I had read
about real numbers.

6. Can you
describe me
about this?
Yes why not?
Thanks.
First you should know
what are two very
important properties of
real numbers.

7. What are these
two properties ?
(1) Euclid’s division
lemma (2)Fundamental
theorem of arithmetic.
What are the
main role of
these properties?
Let 2 positive integers a
and b. There exist unique
integers q and r
satisfying a=bq+r,0<r<b

8. Step (1) We find the whole no. q and r such that c=dq+r,
0<r<d.
Step (2) If r=0,d is the HCF of c and d . If r is not= 0,
apply division lemma to d and r.
Step (3) Continue the process till the remainder is 0.
For example: HCF of 4052 and 12576
Here, 12576=4052.8+420
4052=420 .9+272
420=272.1+148
272=148.1+124
148=24.5+4
24=4.6+0
So, 4 is the HCF of 12576 and 4052.

9. According to this theorem , every
composite number can be expressed as
a product of prime and this
factorization is unique apar from the
order in which prime factors occur.
For example, 32760=2.2.2.3.3.5.13
It is very easy. Now tell me
about Fundamental
theorem of Arithmetic.
Yo! I understand very
formly about real
numbers. Thanks.