Mathematics Game

Given Array := {1,2,3,4,5,6,7,8,9,10}

Get four numbers from the Array. For example: {1,3,5,8} or {1,1,3,8} or {2,2,2,2} …

So IMO there are 10*10*10*10 cases.

Then do a calculate of the four numbers with the basic operators: ADD,MINUS,MULTIPLY,DIVIDE

The operators can be duplicated.

For example: given {1,3,5,8}, We can calculate it like:

• 1*3*5*8 = 120
• 1*3*5/8 = 1.xxx
• (1+3)*5-8 = 12
• (1+3)*(5-8) = -12

Question:  Give a integer N(0<N<10001), count how many times when the calculated result is equaled to N. And show the equality.

I think there might be two different answers. Considering the cases below, we could identify them as the same or the difference.

• ((1+2)+3)*6 = 36
• ((2+1)+3)*6 = 36