day/dydd 37 at 7puzzleblog.com

T he Main Challenge

If you add 1+4, then to that answer add 9, then keep on adding consecutive square numbers to the previous total, what is the first answer you reach that is greater than 200?

(Hint: Square numbers are 1 (1×1), 4 (2×2), 9 (3×3) … and so on.)

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 1st & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

What is the sum of the factors of 30 listed above?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are THREE ways of making 37 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

The Target Challenge

Can you arrive at 37 by inserting 1, 3, 5 and 7 into the gaps on each line?

•  ◯×◯+◯– = 37
•  (◯+◯)×◯+ = 37
•  (◯+◯)×◯– = 37
•  ◯²–◯×(◯–◯) = 37
•  ◯²+◯×(◯–◯) = 37