# DAY/DYDD/GIORNO/NAP 35: Th e Main Challenge

÷2   1   ×5   5   ×3   6   ÷2   3   ÷3   ×2

10   +6   ×3   6   ÷2   +3   ÷3   +2   –4   ×6   =   ? 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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

Which six numbers above can be made by adding two others from 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 TWO ways of making 35 when using Lagrange’s Theorem. Can you find both? The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which are the THREE numbers it is possible to make from the list below?

11    22    33    44    55    66    77    88    99    110

#11TimesTable

The Target Challenge

Can you arrive at 35 by inserting 3, 4, 5 and 8 into the gaps on each line?

•  (◯+◯◯)× = 35
•  (◯+◯)×+ = 35
•  ◯³–×◯– = 35   