I go with 4.
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Although 1,5,13 is a recognized sequence, being given only 2 values of a sequence I would argue there is actually no correct arithmetic answer as there is nothing other than elegance to solve for. Unlike the original challenge.
3 fits in that sequence also therefore x could equal 9
Now, how does one 'add' -21?
The minus sign means that you subtract 21 from the other total.
So in the original question 28 + 29 = 57 57 - 21 = 36 The square root of 36 is 6 (6 x 6 = 36)
Perhaps too elegant a challenge.
I was picking up Fuzzie's request for a challenge involving prime numbers.
5 and 13 are both prime, the third number, while not a prime involves solving a right triangle.
Perhaps for that challenge the given sequence should just be x,25,49,121,169. Providing the sqrt() clue being redundant?
BTW, Ian your challenge beat me. The sqrt() function actually made it solving the problem given 3 elements not 2! My bad.
12.
5, 12, 13 where 5 and 12 are the sides of a triangle adjoining the right angle and 13 is the hypotenuse.
In a right angled triangle, the sum of the squares of the 2 sides equals the square of the hypotenuse. (5x5) + (12x12) = (13x13)
It is along time since I learned that t high school but has stuck as has 3,4,5 for the same purpose.
I have been following this thread with interest. I admit I'm lost with all the prime and SQRT lingo, but I'll make my contribution.
When I was building and servicing CNC machines I had to learn Hex.
First 10 prime numbers in Hex.
2
3
5
7
B
D
11
13
17
1D
And in Octal
2
3
5
7
13
15
21
23
27
35