DAY/DYDD/GIORNO/NAP 113:

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 2 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?

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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