# DAY/DYDD/GIORNO/NAP 125: T he Main Challenge

Using the numbers 3, 4 and 5 just once each, and with + – × ÷ available, only FOUR of the numbers on the list below are possible to achieve. Which ones are they?

1    3    6    9    10    12    15    18    21    24    27    30

Full details of our popular arithmetic & strategy board game can be found at it’s own dedicated website. 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 & 7th rows contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

Which multiple of 5, when subtracting 4 from it, becomes a square number? 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 SEVEN ways of making 125 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which TWO 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 125 by inserting 5, 10, 15 and 20 into the gaps on each line?

•  ◯×◯+◯+◯ = 125
•  ◯×◯–◯×◯ = 125
•  ◯²–◯×(◯–◯) = 125
•  (◯+◯)×(◯–◯) = 125
•  ◯×◯+◯+double◯ = 125   