# day/dydd 43 at 7puzzleblog.com T he Main Challenge

Using the numbers 2, 4 and 6 once each, with + – × ÷ available, find the SIX target numbers from the following list that are mathematically possible to make:

12    14    16    18    20    22    24    26    28    30 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 & 6th rows contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

What is the sum of the cube numbers? 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 THREE ways of making 43 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

4    8    12    16    20    24    28    32    36    40

#4TimesTable

The Target Challenge

Can you arrive at 43 by inserting 4, 5, 8 and 9 into the gaps on each line?

•  ◯×–◯÷◯ = 43
•  ◯²+◯×(◯–◯) = 43
•  (◯+◯)×–◯² = 43
•  (×√×√)– = 43
•  (–√+ = 43   