### Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

### Plants

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

### Gran, How Old Are You?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

# Count the Digits

##### Stage: 1 and 2 Challenge Level:

We can do all sorts of things with numbers - add, subtract, multiply, divide ...

Most of us start with counting when we are very little. We usually count things, objects, people etc. In this activity we are going to count the number of digits that are the same.

Rule 1 - The starting number has to have just three different digits chosen from $1, 2, 3, 4$.
Rule 2 - The starting number must have four digits - so thousands, hundreds, tens and ones.
For example, we could choose $2124$ or $1124$.

So when we've got our starting number we'll do some counting. Here is a worked example.

Starting Number

We then count in order the number of $1$s, then the number of $2$s, then $3$s and lastly $4$s, and write it down as shown here.

So the first count gave one $1$, one $3$ and two $4$s.
You may see that this has continued so the third line shows that the line above had three $1$s, one $2$, one $3$ and one $4$.
The fourth line counts the line above giving four $1$s, one $2$, two $3$s and one $4$.

And so it goes on until ... until when?
Your challenge is to start with other four digit numbers which satisfy the two rules and work on it in the way I did.
Tell us what you notice.

What happens if you have five digits in the starting number?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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