# day/dydd 11 at 7puzzleblog.com

The Main Challenge

Today’s task is to arrive at the target number of 7 by using the four numbers 7, 7, 7 and 7 once each. All four arithmetic operations + – × ÷ are available. Can you do it?

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 & 6th rows contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

From this list, what is the sum of the square 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 is only ONE way to make 11 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

The Target Challenge

Can you arrive at 11 by inserting 2, 3, 4 and 5 into the gaps on each line?

•  ◯×◯+◯–◯ = 11
•  ◯÷◯×◯+◯ = 11
•  ◯²(◯×(◯+◯)) = 11

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