# DAY/DYDD/GIORNO/NAP 74: T he Main Challenge

Can you arrive at the target answer of 24 by using the digits 2, 9, 13 and 13 exactly once each and 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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Which three numbers, when each is multiplied by 4, have their answers on the list? 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 FIVE ways of making 74 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which THREE numbers are not possible to make from the list below?

12    24    36    48    60    72    84    96    108    120

#12TimesTable

The Target Challenge

Can you arrive at 74 by inserting 4, 6, 7 and 8 into the gaps on each line?

•  ◯×◯+◯× = 74
•  (◯+◯)×◯–◯² = 74
•  (◯+◯)×◯+ = 74   