day/dydd 96 at 7puzzleblog.com

T he Main Challenge

Study the seven clues below and place the numbers 1-9 into the nine positions. Each number should appear exactly once in this grid.

x              x              x

x              x              x

x              x              x

Clues:

1.  The 1 is directly left of the 9,
2.  The 9 is directly above the 6,
3.  The 6 is further right than the 4,
4.  The 4 is directly right of the 8,
5.  The 8 is directly above the 2,
6.  The 2 directly left of the 5,
7.  The 5 is not next to the 7.

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 1st & 3rd rows contain the following fourteen numbers:

2   9   13   14   15   22   25   36   40   42   45   66   72   80

What is the difference between the highest and lowest 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 of making 96 when using Lagrange’s Theorem. Can you find it?

Can you arrive at 96 by inserting 2, 3, 5 and 6 into the gaps on each line?

•  (◯+◯)×◯×◯ = 96
•  (◯×◯+◯)×◯ = 96
•  ◯³+◯²+◯–◯² = 96
•  (◯+◯)²–(◯+◯)² = 96
•  (◯+◯)²+◯²–◯² = 96

Answers can be found here.

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