Sigmund

Sigmund is a deductive reasoning game that uses all the numbers from 1 through 9 in a 3 by 3 square grid. Your job is to arrange the nine numbers in the square using all of your powers of logic. You will be given clues that represent part of the 3 by 3 game board. Each box contains a clue that tells what numbers could go in the box. Be careful, the clues themselves might be able to fit in different places on the game board.

Here are the clues that you might see in a Sigmund game:

E	The number that goes in this space is an even number.
E	The number that goes in this space is not an even number.
P	The number that goes in this space is a prime number (Hint: Don't forget that 1 is not prime!)
P	The number that goes in this space is not a prime number (so it is either 1 or it is a composite number).
	The number that goes in this space is a square number (look below for more information on square numbers).
	The number that goes in this space is a triangular number (look below for more information on triangular numbers).
	The number that goes in this space is a cubic number (these are numbers that are perfect cubes. Do you know what 2 numbers are perfect cubes?).
5	The number that goes in this space is given to you. In this case, the number 5 goes in this space.

There are numbers that are called Figurate numbers because they form different figures, including squares, triangles, and cubes. Square numbers can make a square (they are also the perfect squares if you learned about them). For example:

? ? ? ? ? ?

? ? ? ? ?

? ? ?

The first three square numbers are 1, 4, and 9 (or 1 2 , 2 2 , 3 2 ). How about triangular numbers?

? ? ?

? ? ? ?

? ? ?