1. ## Master Lock Combination

Ok, I have this lock and can't remember the combination. It's the standard Master Lock with 3 numbers in the combination and the numbers are 0 - 39. However, I do remember all three of the numbers are either 10,15,20,25,30, or 35. And none of the numbers are repeated. Can anyone think of good way to go about going through all the possibilities?

2. Originally Posted by cowmoonrock
Ok, I have this lock and can't remember the combination. It's the standard Master Lock with 3 numbers in the combination and the numbers are 0 - 39. However, I do remember all three of the numbers are either 10,15,20,25,30, or 35. And none of the numbers are repeated. Can anyone think of good way to go about going through all the possibilities?

I don't know if there is a good way to approach this...for there are 720 different combinations!

--Chris

3. Hello, cowmoonrock!

I have this lock and can't remember the combination.
It has 3 numbers in the combination and the numbers are 0 - 39.
However, I do remember all three of the numbers are either 10,15,20,25,30, or 35.
And none of the numbers are repeated.
Can anyone think of good way to go about going through all the possibilities?
There are: . $6\cdot5\cdot4 \:=\:120$ possible choices.

To crank through all the combinations . . . call the six numbers: $a,b,c,d,e,f$

Use the first two: . $a\,b\,\_$
For the third, cycle through the other four numbers: . $\begin{array}{c}ab{\color{blue}c} \\ ab{\color{blue}d} \\ ab{\color{blue}e} \\ ab{\color{blue}f}\end{array}$

Change the second number: . $a\,c\,\_$
For the third, cycle through the other four numbers: . $\begin{array}{c}ac{\color{blue}b} \\ ac{\color{blue}d} \\ ac{\color{blue}e} \\ ac{\color{blue}f} \end{array}$

Similarly, we have: . $\begin{array}{c}adb\\adc\\ade\\adf\end{array} \quad \begin{array}{c}aeb \\aec \\ aed \\ aef \end{array}\quad \begin{array}{c}afb \\ afc \\ afd \\ afe \end{array}$

And we have the 20 that begin with $a.$

To find the 20 that begin with $b$ . . .

Begin with: . $b\,a\,\_$
Cycle through the other four numbers: . $\begin{array}{c}ba{\color{blue}c} \\ ba{\color{blue}d} \\ ba{\color{blue}e} \\ ba{\color{blue}f} \end{array}$
Then: . $\begin{array}{c}bca\\bcd\\bce\\bcf\end{array} \quad\begin{array}{c}bda\\bdc\\bde\\bdf \end{array}\quad\begin{array}{c}bea\\bec\\bed\\bef \end{array}\quad\begin{array}{c}bfa\\bfc\\bfd\\bfe \end{array}$

And so on . . .