I have a sheet formated somewhat like this
 Thing         5  6  7  Person 1  Person 2   Person 3 
 Thing 1          1  2      7         7          6
 Thing 2          5                   5 
 Thing 3          7         6         6
 Thing 4          6         6         5         
I am trying to find a query formula that I can place in the columns labeled 5,6,7 that will count the number of people who have that amount of Thing 1. For example, I filled out the Thing 1 row, showing that 1 person has 6 of Thing 1 and 2 people have 7 of Thing 1.
 
                        
You can use this function: "COUNTIF". The formula to write in the cells will look like this:
For more information regarding this function, check the documentation: https://support.google.com/docs/answer/3093480?hl=en