# day/dydd 129 at 7puzzleblog.com T he Main Challenge

With the four arithmetical operations + – × ÷ available, use all four numbers 1, 1.5, 3 and 4 once each in your attempt to arrive at the target answer of 7. 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 2nd & 4th rows contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

Which four different numbers from the above list have a sum of 100? 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 129 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which SIX numbers is it 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 129 by inserting 3, 8, 9 and 12 into the gaps on each line?

•  ◯²+◯–◯×◯ = 129
•  ◯×(◯+◯)–√◯ = 129
•  double(◯²)+◯÷(◯+◯) = 129   