Can You Solve This Brilliant Math Pattern Puzzle?

If 2=6, 3=12, 4=20, 5=30 and 6=42, what does 9 equal ?

This question is basically the application of patterns and sequences. These types of questions can be easily solved if one tries to observe the pattern being followed...

If we observe the pattern carefully ... In each set, the integer before the equal sign is multiplied by its consecutive next integer greater than it, and the result is on the other side of the equal sign.

If the LHS is represented as "A" then RHS can be calculated using the expression => A*(A+1)

for example, in the first set, the integer before the equal sign is 2 which is multiplied by its consecutive next integer greater than it which is 3, and the result is 6 which is on the other side of the equal sign.

in the second set, the integer before the equal sign is 3 which is multiplied by its consecutive next integer greater than it which is 4, and the result is 12 which is on the other side of the equal sign.

applying this pattern, the series looks like

**2 = 6 → 2 x 3 = 6**

**3 = 12 → 3 x 4 = 12**

**4 = 20 → 4 x 5 = 20**

**5 = 30 → 5 x 6 = 30**

**6 = 42 → 6 x 7 = 42**

therefore:

**7 = 56 → 7 x 8 = 56**

**8 = 72 → 8 x 9 = 72**

**9 = 90 → 9 x 10 = 90 is the final solution.**

observing the pattern the answer is 90.

There are multiple patterns that satisfy the pattern, I will explain one another pattern.

Here, the first number is what we are given and the second number is what is hidden. Here by taking a close look we will see that the pattern is decoded as

RHS = x+x^2

where x is the number in the LHS

So, by applying this pattern we can actually see the things happening...

for example, in the first set, the integer before the equal sign is 2 hence x is 2, after applying the value in pattern RHS is 2+2^2 = 6

**2 + 2^2 = 2 + 4 =6**

Similarly in the second set

the integer before the equal sign is 3 hence x is 3, after applying the value in pattern RHS is 3+3^2 is 12

**3 + 3^2 = 3 + 9 =12**

applying the same pattern to 9, the solution is 9+9^2 which results in 90

**→****9 +9^2 = 9 + 81 =90**The answer could have been different if we take the pattern alternatively. do share your answer in the comment sections if you found a different pattern that satisfies here.

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ReplyDeleteVery Good Puzzle with a good explanation.

ReplyDeleteGood Work :)