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MathMagic Cycle 11: Level 7-9 Regular
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I received a magazine that accidentally hadn't been stapled, and
when I took it out of the envelope, out came pages 6 and 19 as a
double sheet. Since some friends were laughing at my magazine, I
told them I was able to predict not only what other pages were on
the sheet I had in my hand, but exactly how many pages the magazine
had. What did I have to do to in order to be correct? By working
several different pages, can you develop a way of telling regardless
of the number of pages?
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MathMagic Cycle 11: Level 7-9 Advanced
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( ) Crossed Z Hexagon:
/ | \
( )--+--( ) Try placing the numbers 1 to 6 in the vertices of
| | /| of the hexagon, so that consecutive numbers (2 and
| | / | 3 or 5 and 6) are NOT joined by a line.
| |/ |
| * | How many ways of placing the numbers are there?
| /| |
| / | | If the vertical center line wasn't there, how many
( )--+--( ) arrangements would be possible?
\ | /
( )
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Good luck