#741 - Matchsticks Number Sequence Puzzle
What is the next number in the matchsticks number sequence below?
What is the next number in the matchsticks number sequence below?
If,
Sachin + Ramesh + Tendulkar = 6
Sachin x Ramesh = 2
Ramesh x Tendulkar = 6
Then,
Tendulkar x Sachin =?
3
Sachin + Ramesh + Tendulkar = 6
Sachin x Ramesh = 2
Ramesh x Tendulkar = 6
Given.
Sachin x Ramesh = 2
Ramesh x Tendulkar = 6
Rewriting Both equations in terms of Ramesh,
Sachin = 2/Ramesh
Tendulkar = 6/Ramesh
Replacing above values in equation "Sachin + Ramesh + Tendulkar = 6"
2/Ramesh + Ramesh + 6/Ramesh =6
(2 + Ramesh^2 + 6)/Ramesh = 6
8 + Ramesh^2 = 6Ramesh
Ramesh^2 - 6Ramesh + 8 = 0
(Ramesh - 4) (Ramesh - 2) = 0
Therefore;
Ramesh = 4 or 2
Let us take value of Ramesh as 2
Sachin = 2/2 = 1
Tendulkar = 6/2 = 3
Therefore;
Tendulkar x Sachin = 3 x 1 = 3
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