*************************************** MathMagic Cycle 10: Level 10-12 Regular *************************************** ( ) 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? \ | / ( ) **************************************** MathMagic Cycle 10: Level 10-12 Advanced **************************************** By adding and subtracting the numbers in the rows below, you can establish relationships. Using the diagram on the left, if the relation- A B C By adding and subtracting numbers in the rows of the 2 6 8 figure on the left, one can establish that one of the 1 3 4 relationships is C - A = B, so finding the values for the 5 4 _ first and third columns should be fairly simple. _ 2 5 Use the same general criteria to establish A B C D E all relationships for the figure on the right 9 0 9 9 0 and find out what numbers go in column E. 5 3 2 8 6 6 2 4 8 _ 7 2 5 9 _ (Thanks to Joe Anton, Houston TX) 2 1 1 3 2 ================== Good luck