# day/dydd 76 at 7puzzleblog.com T he Main Challenge

It is possible to use seven 4’s (4 4 4 4 4 4 and 4) once each, together with the four operations + – × ÷, to make all the different target numbers 1, 2, 3 and 4.

For instance, one way of arriving at the number 1 is:

4 – 4÷4 – 4÷4 – 4÷4 = 1

Can you show how to make the next three target numbers 23 and 4? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

What is the sum of the multiples of 9? 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 76 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which TWO numbers is it 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 76 by inserting 6, 8, 10 and 12 into the gaps on each line?

•  ◯×◯+(◯◯)² = 76  (2 different ways)
•  ◯×◯–(◯÷◯)² = 76
•  ◯×(◯)+◯² = 76   