# day/dydd 23 at 7puzzleblog.com

The Main Challenge

To solve this Octaplus puzzle, find the values of eight letters, A to H, from the given clues. Each letter contains a different whole number in the range 1-50:

1.  B minus E is either 14 or 15,
2.  C is one-quarter of B,
3.  F is one-seventh of E,
4.  D is half of B,
5.  G is H plus C,
6.  one-third of E is an odd number,
7.  H is one-third of D,
8.  A is 150 minus the sum of the other seven numbers.

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 2nd & 4th rows contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

How many square numbers are listed?

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 of making 23 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

30    31    32    33    34    35    36    37    38    39

#NumbersIn30s

The Target Challenge

Can you arrive at 23 by inserting 2, 3, 4 and 6 into the gaps on each line?

•  ◯×◯+◯–◯ = 23
•  (◯³–◯×◯)÷◯ = 23
•  (◯²+◯)–(◯³+◯²) = 23