## Hints for playing the Number Game

It helps to make notes, on paper, or in the optional workspace we gave you.

How to make up guesses:
- It speeds things up if you change more than one digit from one guess to the next, in the early stages,
though your deductions get more complicated
- If your first two guesses were 12345 - 3 - 1, 34567 - 3 - 0, then 45=67, so if both 45 then both 67,
if one of 45 then one of 67, if not 45 then not 67. Your third guess could include 456 and 7 (with one of 123),
so if you got four or five right then you'd know all four of 4567 were right, two or three right then one of each
and so on.
- The secret numbers are completely random, so it will help you if your first guess is not complicated,
i.e. 12345 is probably better to visualise than 59276 when it comes to making logical deductions

To get the right digits:
- If 12345 gives 1 right, then 67890 would give 4 right
- If, for example, you had two guesses: 12345 = 3 right, 34567 = 4 right,
this means that 67 has one more digit than 45 in the answer.
So, if both 67 were right, then one of 45 would be right, and 2 of 123, and 890 would be wrong,
**OR** one of 67, both 45 are wrong, two of 123 and 1 of 890 would be in the answer

To get the right positions:
- For each guess after the first, where you have some digits the same,
make sure you change the order of all or most digits to give more information
- when you know the right digits, it may help to make a table for all digits with 5 columns representing the positions.
You can put an x in any column in that table, where a digit can not go,
so e.g. if 12345 gave 4 right with 0 in the right position, 1 cannot be 1st, 2 cannot be 2nd and so on.
Sometimes it can even help you before you know all the right d igits

Finally - everybody has their own way of doing things, so none of these hints may be right for you!