It is true for these three sets of numbers, but is it always true?
To prove whether it is always true, I have to use some algebra.
Call the first number “a” and the second number “b”.
If it is true then I need to show that:
2(a 2 + b 2 ) = (a + b) 2 + (a – b) 2
Expanding the brackets on the right hand side of the equation:
(a + b) 2 + (a - b) 2 = a 2 + 2ab + b 2 + a 2 – 2ab + b 2 = 2a 2 + 2b 2 = 2(a 2 + b 2 )
This is what I wanted to prove.
So, using algebra, we can prove that this theory works for any two numbers.
Thank you for reading!
Answers to Puzzles 1. Two or three of them. 2. 655+655=1310 or 855+855=1710 3. Yes. 1st, 4th, 6th, 7th in one group, 2nd, 3rd, 5th, 8th in the other. 4. 132
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