Quandaries
and Queries 

Who is asking: Parent Level: Elementary Question: 

Hi Lisa, Here is a procedure to generate lots of equations:
Note that this procedure produces 5 possibilities. By being careful not to generate duplicates, we can repeat the procedure using a different arrangement of 0,1,2,3 and 4. Provided we change the order, this will produce distinct possibilities. For example:
Again, this produces a list of 5 distinct possibilities. We can do the above procedure, and always produce 5 distinct possibilities, using the following arrangements of 0, 1,2, 3 and 4 as the starting number:
Each of these 24 possible starting numbers produces 5 distinct possibilities, so we have now generated a list of 24x5=120 distinct possibilities. It is easy to double this list by swapping digits between the two numbers. For example, swapping the first digits of
Swapping the first digit for each of the 120 already generated produces 120 more distinct possibilities. So we now have 240, which is more than the required 150+ required, so I'll quit. But it should be mentioned that there are a heck of a lot more possibilities than 240. To find how many requires a careful counting procedure, which is probably beyond the ability of a grade 4 student to comprehend. Being careful not to generate duplicates there are (10x8x6x4x2)/2=1920 distinct possibilities. Paul 

