Video summary
In this mathematical challenge, viewers are invited to select any number between one and ten and perform a specific sequence of operations on it. The process begins by doubling the chosen number and then adding six to the result. Following this, the new total is divided by two, and finally, the original number selected at the start is subtracted from the current answer. The central question posed is whether this final result remains constant regardless of which number between one and ten is initially chosen.
To solve this puzzle, the video first demonstrates the process using a concrete example where the number five is selected. By doubling five to get ten, adding six to reach sixteen, dividing by two to obtain eight, and then subtracting the original five, the result is three. The presenter then suggests that instead of testing every single integer individually, one can use algebraic representation to understand why the outcome is always the same for any input number within the given range.
By representing the unknown number as a variable 'a', the steps are translated into an algebraic expression: doubling gives 2a, adding six results in 2a + 6, and dividing the entire sum by two simplifies to a + 3. The final step involves subtracting the original variable 'a' from this expression, which cancels out the variable entirely and leaves only the constant value of three. This algebraic proof confirms that no matter what number is chosen between one and ten, the mathematical operations will always yield the same answer.
The conclusion of the session highlights the elegance of algebra in simplifying numerical patterns, showing that complex-looking arithmetic sequences can often reduce to simple constants. The video successfully demonstrates that the specific combination of doubling, adding six, halving, and subtracting the original number is designed specifically to eliminate the variable, ensuring a consistent result of three for every possible input. This exercise not only solves the challenge but also illustrates how mathematical rules apply universally across different numbers within a set.
Read the full video transcript
Hello and welcome to the session. In
this session, we are going to solve a
mathematical challenge. Think of a
number between 1 to 10. Double it and
add six. Now divide it by two and then
subtract the number you initially
thought of from the answer.
What number do you get? Is your answer
same for every number between 1 to 10?
If yes, then why?
Before solving this challenge, let me
give you some hints which may help you
in solving this challenge.
First, this challenge is based on
addition, subtraction, division, and
multiplication of numbers within 10.
Here we have to tell whether we get the
same number for every number chosen
between 1 to 10. So here we will
consider any number between 1 to 10 as a
that is
a can be
any number
say
1
or 2
or 3
or 4 and so 1 or 10.
Also when we multiply a with any number
say 2, we will write it as
2 * a
that is
2 a.
Similarly when we divide a by any other
number say three then we write it as
a divided by 3 that is
a by 3. So using these hints try and
complete the challenge. Observe the
statement carefully.
Think of any number between 1 to 10 and
do the calculations as guided in the
challenge and see what number you
obtain.
You may pause the video to try it
yourself.
Were you able to find it? Let me help
you. In this challenge, we have to think
of a number between 1 to 10. So, let us
start with any number between 1 to 10.
Suppose
we choose
five.
Now, according to the challenge, we have
to double it.
that is 2 *
5 which is equal to 10.
Then the challenge says double it and
add six.
So after we have doubled five we have to
add six in the obtained number.
So we add 6 to 10 that is 10 + 6 = 16.
Now we have to divide it by 2. So we
divide the obtained number by two and
get 16 /ed by 2 equal to 8.
Now we have to subtract
the number
we have thought of
from this number.
That is we have to subtract 5 from 8. we
get 8 - 5 = 3.
Now we have to check whether we get the
same number for every number between 1
to 10.
That is we have to check if we take any
number say 1 or 2 or 3 or 4 or 6 or 7 or
8 or 9 or 10
and perform the same operations
we always get our answer three or not.
So instead of taking each number one by
one, let us represent any number
between
1 to 10 as a.
So now we have to double it that is 2 *
a
which is equal to 2 a. Now we have to
add six to the obtained number. So we
get 2 a + 6.
Now it has to be divided by two. So we
get
2 a + 6 divided by 2 which is equal to 2
a + 6 by 2 which is equal to 2 a by 2 +
6 by 2 which is equal to a + 3.
as 2 a by 2 is 8 and 6 by 2 is 3.
Now we have to subtract
the number we had thought of initially
that is a.
So we get a + 3
minus
a which is equal to 3.
Is that not amazing?
Whatever number we choose between 1 to
10, we will always get our answer as
three. That was indeed easy.
So with this we have completed our
challenge. Hope you enjoyed solving the
challenge.