# DAY/DYDD/GIORNO/NAP 185: T he Main Challenge

Your task is to arrive at the target answer of 7 when using each of the numbers 0.7, 2, 7 and 10 exactly once each, with +  × ÷ available. The 7puzzle Challenge

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

The 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

How many multiples of 3 are present? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 185, in NINE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which SEVEN numbers is it possible to make from the list below?

1    3    6    10    15    21    28    36    45    55    66

#TriangularNumbers The Target Challenge

Can you arrive at 185 by inserting 5, 1520 and 30 into the gaps on each line?

•  ◯+◯×◯+◯ = 185
•  ◯×(◯–◯)–half◯ = 185   