Briefcase lock
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
Age
5 to 7
Challenge level
Problem
Image
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8, but not what order they go in.
How many possible combinations are there to try?
Getting Started
If $8$ is the first digit, what numbers are possible?
What could be the first digit instead of $8$?
What could be the first digit instead of $8$?
Student Solutions
Josh from Befordshire says:
There are six combinations possible. Because there are three different numbers, you multiply $3$ by $2$ and then by $1$, which makes $6$.
Joshua says:
I think the answer is six combinations and how I did it was I wrote down all the correct combinations:
358
385
538
583
835
853
Jianmin (Henry Park Primary, Singapore) agrees with six combinations, using $3$ x $2$ x $1$.
Teachers' Resources
Why do this problem?
This problem is a good context in which to encourage children
to work systematically to find all possibilities.
Key questions
If $8$ is the first digit, what numbers are possible?
What could be the first digit instead of $8$?
How do you know you have all the possibilities?
Possible support
If children are struggling to find a system, invite them to
write down different possible numbers on separate pieces of paper.
Once they have thought of as many as they can, work with them to
sort the numbers so that a pattern emerges and a structure is
imposed. In this way, learners will be able to spot any gaps for
themselves.