SOLUTION: Think of a number. Add 4. Multiply by 2. Subtract 6. Divide by 2. Subtract the number you started with. The answer is always one. How can I show why it must be true that f

Question 32532: Think of a number.
Add 4.
Multiply by 2.
Subtract 6.
Divide by 2.
Subtract the number you started with.
The answer is always one.
How can I show why it must be true that for any number used in the first step always yield 1? or I need to find a number for which the HDP fails.
I also need to know how to come up with my own, more complicated procedure that always gives the answer one. Can you help?
Answer by Fermat(136) (Show Source): You can put this solution on YOUR website!
Think of a number: x
Add 4: x+4
Multiply by 2: 2(x+4) = 2x + 8
Subtract 6: 2x + 2
Divide by 2: x + 1
Subtract the number you started with: 1
The above should show you how the answer is always one. The numbesr you first start with is manipulated so that it is removed and the result (1) is then constant.
You can make up your own procedure by deciding upon a result value and then working backwards by applying operations such that you end up with a "number" i.e. x.
e.g. let the result be 1.
Multiply by a number: x
double it: 2x
Add on 2: 2x + 2
half it: x + 1
take away 1: x
You have operated on the result (1) nad ended up with a "number".
Now reverse the procedures, so that you start with a number (x) and always end up with the same result (1).
Think of a number: x
add on 1: x + 1
double it: 2x + 2
take away 2: 2x
half it: x
divide by the number: 1 <- always the answer
Sorry, I don't know what HDP means.
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