# day/dydd 113 at 7puzzleblog.com

T he Main Challenge

Here is a unique 7-part question. Answer all seven parts:

1.  (4 + 3) + (2 – 1)  =  ?
2.  (4 × 3) ÷ (1 × 1)  =  ?
3.  (4 – 3) × (2 ÷ 1)  =  ?
4.  (3 + 3) ÷ (2 × 1)  =  ?
5.  (3 ÷ 3) – (1 + 1)  =  ?
6.  (3 – 3) × (1 ÷ 1)  =  ?
7.  (3 × 3) – (2 + 1)  =  ?

What is the sum of all seven answers?

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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

What is the difference between the two multiples of 8?

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 FIVE ways of making 113 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

The Target Challenge

Can you arrive at 113 by inserting 7, 10, 12 and 14 into the gaps on both lines?

•  ◯×◯+◯–◯ = 113
•  ◯²–(◯+◯+◯) = 113

Answers can be found here.

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