Page 62 - Maths Skill - 6

60 Maths

Now, taking 4-digit number is 3087
P = 8730

Q = 0378
R = 8730 – 0378 = 8352
R ≠ 6174
So, again repeat this concept

Now, taking 4-digit number is 8352
Here, P = 8532
Q = 2358
R = P – Q = 8532 – 2358 = 6174

Here, process completed.

THE COLLATZ CONJECTURE (AN UNSOLVED MYSTERY)
In 1937, The German Mathematician Lothar Collatz conjectured that the sequence will always reach 1, regardless
the whole number you start with.
According to this conjecture, a sequence is prepared by the rule that one starts with any number. It the number is
even then take half of it and go ahead. But the number is odd then multiply that odd number by 3 and add 1 into
it and again repeat the above process.
Let’s understand the above concept with the help of following sequence

(i) Even number Even number Odd number Even
12 6 3 10 5
÷ 2 ÷ 2 3 × 3 + 1= 10 ÷ 2

Even Even Even Odd
2 4 8 16
Randomly Even ÷ 2 ÷ 2 ÷ 2 5 × 3 + 1
choosen ÷ 2
1

Process completed, if 1 comes (obtained)
So, the series is 12, 6, 3, 10, 5, 16, 8, 4, 2, 1

(ii) 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1

(iii) 21, 64, 32, 16, 8, 4, 2, 1

Beside this, it is still only conjecture. Even today, many Mathematicians working on it, it remains an unsolved
problem as to whether Collatz’s conjecture is true!
Collatz’s conjecture is one of the most famous unsolved problems in maths.

ESTIMATION
The estimation of a number is a reasonable guess of the actual value. Estimation means approximating a quantity
to the accuracy required. This is done by rounding off the numbers involved and getting a quick and rough answer.