Brain Teasers
Squares
The square of one whole number minus the square of another whole number equals 73.
What are the two numbers? This can be done by trial and error but a little mathematical knowledge and maybe some algebra will get the answer fast.
What are the two numbers? This can be done by trial and error but a little mathematical knowledge and maybe some algebra will get the answer fast.
Hint
73 is similar 41,29,19 etc.Answer
The two numbers are 37 & 36. Therefore (37x37)1369 minus (36x36)1296 = 73. The number 73 is a "prime" number i.e. the only two multiples for it are "73" & "1". By algebra, x2-y2 = 73 which is (x+y)(x-y)=73. One of those two numbers must be "1". It can't be x+y (that would be more than "1") so it must be x-y=1. By simple substitution the answer is revealed.Hide Hint Show Hint Hide Answer Show Answer
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Comments
i suck at math!
Actually, there is an even easier expanation.
The difference between the squares of any two consecutive numbers is equal to the sum of those two numbers.
For example, consider 7 and 8. The square of 7 is 49. The square of 8 is 64. 64 - 49 = 15. 7 + 8 = 15.
So all you need to do is subtract 1 from 73, then divide by 2. 73 - 1 = 72. 72 / 2 = 36. The numbers are 36 and 37.
This formula works for prime and non-prime numbers.
The difference between the squares of any two consecutive numbers is equal to the sum of those two numbers.
For example, consider 7 and 8. The square of 7 is 49. The square of 8 is 64. 64 - 49 = 15. 7 + 8 = 15.
So all you need to do is subtract 1 from 73, then divide by 2. 73 - 1 = 72. 72 / 2 = 36. The numbers are 36 and 37.
This formula works for prime and non-prime numbers.
Yes CNME but you first have to determine that are in fact consecutive numbers. That is where the prime number comes in. If it had been 63 for example it could have been 63 x 1 or 21 x 3. In the second case giving 12^2 - 9^2 = 144 - 81 = 63 as a second possible answer.
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