You have probably all seen the following type of magic problems. \"Pick any number. Add three to your number. Double your result. Add four to that number. Divide the result by 2. Finally subtract your original number. Your result is 5.\" The discussion this week is a two part question. Solution part 1: ((((x+3) * 2) + 4) / 2) - x = ((2x+6+4) / 2) - x = x + 5 - x = 5 // Thus its a constant equation which would always be true.. part 2: By backtracking u can create any number of magic equations.. like: 7 // will be the output = x + 7 - x = ((2x + 14) / 2) - x = ((((x + 3) * 2) + 8) / 2) -x Thus, \"Pick any number. Add three to your number. Double your result. Add eight to that number. Divide the result by 2. Finally subtract your original number. Your result is 7.\" .

1. You have probably all seen the following type of magic problems. "Pick any number. Add three
to your number. Double your result. Add four to that number. Divide the result by 2. Finally
subtract your original number. Your result is 5."
The discussion this week is a two part question.
Solution
part 1:
((((x+3) * 2) + 4) / 2) - x
= ((2x+6+4) / 2) - x
= x + 5 - x
= 5
// Thus its a constant equation which would always be true..
part 2:
By backtracking u can create any number of magic equations.. like:
7 // will be the output
= x + 7 - x
= ((2x + 14) / 2) - x
= ((((x + 3) * 2) + 8) / 2) -x

2. Thus,
"Pick any number. Add three to your number. Double your result. Add eight to that number.
Divide the result by 2. Finally subtract your original number. Your result is 7."