# DAY/DYDD/GIORNO/NAP 115: T he Main Challenge

+2   ÷4   +1   ×4   –1   ×5   –16   ×2   –19   +1

÷10   +7   ×4   –16   ÷3   –1   ×5   –8   ×2   +7   =   ?

What is the final answer to this 20-step number trail? 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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

What is the sum of the even numbers? 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 SIX ways of making 115 when using Lagrange’s Theorem. Can you find them all? The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

1    3    6    10    15    21    28    36    45

#TriangularNumbers

The Target Challenge

Can you arrive at 115 by inserting 5, 6, 8 and 9 into the gaps on both lines?

•  (◯+◯+◯)×◯ = 115
•  ◯²+◯×◯+◯ = 115   