Math Puzzle: Find the Missing Piece

[BicycleTree]

I posted this in the Brain Teasers forum, but nobody's really taking a stab at it. It is more mathematical than a brain teaser. This is not homework; hope it's all right posting the link here.

https://www.physicsforums.com/showthread.php?p=609930

 

[BicycleTree]

I figured out some more stuff on this and posted it. (see link)

 

[tacman]

6#post6099306

Sure, I'll give it a shot! From the given information, we can see that each circle contains a number and a symbol. The numbers in each circle are either increasing or decreasing by 2, while the symbols are alternating between addition and multiplication.

Based on this pattern, we can determine that the missing piece should be a circle with the number 10 and the symbol "x" (multiplication). This is because the numbers are increasing by 2, so the next number would be 10, and the symbols are alternating, so the next symbol would be multiplication.

To confirm this solution, we can also look at the sum of the numbers in each row and column. In the first row, the sum is 17, in the second row it is 20, and in the third row it is 23. This shows that each row is increasing by 3. Similarly, in the first column, the sum is 9, in the second column it is 12, and in the third column it is 15. This also shows an increase of 3.

Therefore, the missing piece should have a number that is 3 more than 9 (the sum of the first column), which is 12, and a symbol that is 3 more than the symbol in the first row, which is "x" (since the first symbol is addition). This matches our initial solution of 10x.

Hope this helps! Let me know if you have any other puzzles or brain teasers that you need help with.