Train Game Explanation
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All cityrail train carriages have a 4 digit serial number printed on the walls throughout the carriage.
The aim of the train game is to take those 4 digits and apply mathematical operations to them in order to make an expression which equals a predefined target.
This target is normally 10.
Variations
Different people vary on what rules they play with.
Order
Most people require that the game be solved with the digits in the order they are written. However some don't.
Note that allowing order mixing makes the game 4!=24 times easier.
Operations
Everyone accepts the use of +,-,* and /. Once you start using more complicated operations, then it gets controversial, however that's when it gets interesting.
The rule I generally use is that if you can type the solution into a scientific calculator, then it is acceptable.
Using extra operations means that you have a lot more flexibility.
Here are some examples of useful expressions with tricky operations.
- anything^0=1 (except 0)
- 1st root of anything is that anything
- 0!=1
- cos(0)=1
- acos(1)=0
- arbitrary decimal points can be useful e.g. (5+5)*.1+9=10
- cos(x!)=1 for all x>5 (in degrees)
- sin(x!)=0 for all x>5 (in degrees)
- cos(x!!)=1 for all x>2 (in degrees)
- sin(x!!)=0 for all x>2 (in degrees)
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