# day/dydd 40 at 7puzzleblog.com

T he Main Challenge

In all four groups below, it is possible to make 24 by using the four numbers once each, with + – × ÷ available. Can you show how to achieve the target number of 24 in each case?

•    3   3   3   3
•    4   4   4   4
•    5   5   5   5
•    6   6   6   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 1st & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

What is the sum of the multiples of 6 listed above?

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 just TWO ways of making 40 when using Lagrange’s Theorem. Can you find them both?

The Mathematically Possible Challenge

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

70    71    72    73    74    75    76    77    78    79

#NumbersIn70s

The Target Challenge

Can you arrive at 40 by inserting 2, 4, 5 and 10 into the gaps on each line?

•  (◯+◯–◯)×◯ = 40
•  (◯–◯)×◯×◯ = 40
•  ◯²×◯²×◯÷ = 40

Answers can be found here.

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