day/dydd 206 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:

x              x              x

x              x              x

x              x              x

Clues:

1.  The 8 is directly right of the 9,
2.  The 9 is directly above the 6,
3.  The 6 is directly right of the 4,
4.  The 4 is higher than the 1,
5.  The 1 is further right of the 3,
6.  The 3 is lower than the 7,
7.  The 7 is directly above the 5.

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 2nd & 5th rows of the playing board contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

What is the biggest difference between two consecutive numbers on the above list?

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 NINE different ways to make 206 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 57 and 11 once each, with + – × ÷ available, which is the ONLY number that is possible to make from the list below?

11    22    33    44    55    66    77    88    99    110

#11TimesTable

The Target Challenge

Can you arrive at 206 by inserting 101214 and 18 into the gaps on each line?

•  ◯×◯+◯+◯ = 206
•  ◯×◯+◯+double◯ = 206