# DAY/DYDD/GIORNO/NAP 186: T he Main Challenge

Here’s another 10-step question involving all four arithmetic operations and all numbers from 1 to 10.

• divide by four
• multiply by six
• subtract two
• divide by nine
• multiply by one
• divide by three
• subtract seven 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 2nd & 3rd rows contain the following fourteen numbers:

8   13   17   25   28   36   42   45   48   55   63   64   66   80

What is the difference between the sum of the multiples of 11 and the sum of the prime numbers? 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 186, in NINE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which THREE 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 186 by inserting 346 and 9 into the gaps on each line?

•  (◯×◯+◯)×◯ = 186
•  (◯×◯+double◯)×◯ = 186   