The Puzzle Challenger!!!
This is one is the funny Maths riddle.
here some equations were given,
according to that we have to find the missing number.
Let's find the answer!!!
As per the equation
1+4=1x(4+1)=1x5=5
2+5=2x(5+1)=2x6=12
3+6=3x(6+1)=3x7=21
therefore
8+11=8x(11+1)=8x12=96
So
Answer for this is 96.
We once again get to know the answer of 96, which is somewhat surprising! In fact, the running total with the missing lines generates the same answer, line by line, as the algebraic result from the first approach:
a + b means a + ab = a(1 + b)
How can we see the two approaches are the same? On line 8, there are 7 previous lines. We can make 11 by pairing the first number of each line with the second number of another line: we can pair 1 with 10, 2 with 9, 3 with 8, 4 with 7, 5 with 6, 6 with 5, and 7 with 4. These are 7 pairs of 11. The final line has another 11. This means we need to take 8 and add 11 to it 8 more times, which is 8 + 8(11) = 96.
In general, line n has the equation n + (n + 3), which is equal to the result n + n(n + 3) = n(n + 4).
Let’s prove this formula holds by induction. Assuming the formula is true up to line n, we then consider the next line. In the next line n + 1, we add the numbers (n + 1) + (n + 4). The result in line n is n(n + 4), so when we add (n + 1) + (n + 4) we get:
n(n + 4) + (n + 1) + (n + 4)
= n2 + 6n + 5
= (n + 1)(n + 5)
= (n + 1)[(n + 1)) + 4]
And this completes the induction.
Most people believe the answer is either 96–with the equation a + ab–or 40–with a running total. Since the running total can also get to the answer of 96 when extending the pattern to missing lines, many believe that 96 is the answer that makes the most sense.
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