# day/dydd 234 at 7puzzleblog.com

T he Main Challenge

Using each of the numbers 1.5, 2, 2.5 and 3 once each, and with the four arithmetical operations + – × ÷ available, can you arrive at the target answer of 7 in three different ways?

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 of the playing board contain the following fourteen numbers:

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

List three different numbers that 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 EIGHTEEN different ways to make 234 when using Lagrange’s Theorem. How many of them can you find?

The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

1     8     27     64     125

#CubeNumbers

The Target Challenge

Can you arrive at 234 by inserting 2, 3, 6, 9 and 12 into the gaps on each line?

•  (◯×(◯–◯)+◯)×◯ = 234
•  (◯×◯÷◯+◯)×◯ = 234

Answers can be found here.

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