# DAY/DYDD/GIORNO/NAP 189: T he Main Challenge

Can you insert the numbers 1-9, exactly once each, into the gaps below so that all three lines work out arithmetically?

◯   +   ◯   =   ◯
◯   –   ◯   =   ◯
◯   ÷   ◯   =   ◯ 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

Which number, when 20 is added to it, becomes a square number? 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 189, in ELEVEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable The Target Challenge

Can you arrive at 189 by inserting 3, 4, 5 and 7 into the gaps on each line?

•  ◯×◯×(◯+◯) = 189
•  (◯+◯–◯)³+◯³ = 189   