I have managed to work out an answer to make 200 and have an estimate on how many ways there are to make 200 in the Make 200 problem.
I first started out in using random numbers which was unlikely to work, unless by chance I magically got the answer. By this method, I was not trying to fail but used my failed answer in the "trial and error system" whereby you try an answer and adapt your sum to try and reach the goal.
I worked out that in some way or another you had to have any two answers no matter collum or row add up to 100 so the 4 over all boxes added up to 200.
Next I tried to make 200 using 5 and 0 making 50 in the concept of 50x4=200. This did not work because when you had the 5 an 0 you could put a 0 under the 5 but when you put the number under the 0 you couldn't make 50.
I knew you had to get the bottom row and the right column to each add up to 10. I used 6 and 4 and had a 5 in the top left section of the box. The two row and two column totals each could be added together to equal 120. The total answer equalled 240, 40 away from 200.
I then knew from this information that the total for each side had to be reduced by 20, half of 40. This meant that i had to change the 5 in the top left box to a lower number but keeping the rest so the rows or columns would equal 10.
My answer was top row: 3 6
bottom row:6 4
I think you can make 5 posible answers.