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why does it say "triangular sum", if its sinply the sum of A, B and C?

Im afraid im incredibly frustrated by this one - the preamble seems deliberately difficult to understand (and i have a maths degree, which may be adding to ny frustration).

Please can someone explain what " using the triangular numbers corresponding to the three square terms in each clue..." means - the way i read it, it suggests that each of eg n, m and K in clue VII is triangular - but that cannot be the case.

n equates to the term in the equation 2p + 1 where p is the “root” of a triangular number

For example if n was 15, p would be 7 and the related triangular number would be 28

ah - thanks candledave, that may be the nudge i need (time will tell)!

any idea why "triangular sum" has been used when per cypherhouse, its just a simple sum?

I’m think simply as the sum is a triangular number

thanks candledave - was reading too much into it (and knew it was triangular from prior paragraph)

I'm really not getting this despite a MSc in Maths! I think I have a result for Clue VII such that n < m < K to fit the "square terms given in ascending order" requirement. And as can be seen from the grid, n and m and K are all 2 digits long and also the first digit of m makes the first digit of K, and the first digit of n makes the last digit of K. I also have it so that n^2 + m^2 + K^2 is equal to 2_ _63 where k is a 2 digit number. However, none of this has anything to do with triangular numbers frustratingly! Adding n and m doesn't make a triangular number. Adding n^2 and m^2 doesn't make a triangular number. What aren't I getting?

I tried to help in #42.

Remember that the n and m etc relate to the relevant terms in the complex looking p, q, r and s equation in the preamble

S is triangular and p, q and r are “roots” of triangular numbers

The numbers you have (the grid entries) are as described in the preamble. They are equations of the form

(2p+1)^2 +(2q+1)^2+(2r+1)^2=16s+3

If you work out p,q and r from your answers, then the triangular numbers with those roots, then the integer triple that produces those three triangular numbers when you add any two together, you should find that integer triple adds up to s.

Simple.

I get that, but basically that means that p, q and r can be any integer, because a root of a triangular number can basically be anything. So effectively the only triangular number I need to be concerned about is s?

If you have n and m etc then you have p q and r and the related triangular numbers

As I said before if n is 15, then p is 7 and the triangular number is 28