Vicky's Problem Years 3 - 6 Vicky Nicholson, Aboriginal Education Unit, Tasmania with assistance from Jaye Clair, Debbie Clifford, Joc McConnell ... Margate Homework Centre Sally Oakford, Lize Hall ... East Devonport Primary School Bev Hearps, Becky Murfett ... Penguin Primary School

Investigation

Suppose we turn over the top row of plugs to make them blue. Now down the right hand column we count by 2s and turn over plugs down the column next to that we count by 3s and turn plugs over down the next one by 4s, the next by 5s and the next by 6s. How many rows will it be before we get the first five in a row back again?

Now this diagonal line might be a clue. We could keep it going and keep an eye on what happens when in the other rows. Mmm ... that means we have to put more boards in to keep the top row going. Does that mean we are looking for when we get ten in a row .. or even fifteen in a row back again?

This doesn't look like such a good idea. Keeping that diagonal going means more boards along the top and getting all those back in one one row seems to get further and further away. Let's go back to the original problem and just keep on building until we get the five in a row to appear again.

We did it!! It takes ___ rows before the five in a row comes back!

Extension

We know that it takes ___ rows before the five in a row comes back when you count by 2, 3, 4, 5, 6. Can we work out:

• How many rows before 10 in the top row comes back?
• How many rows it takes for any number in the top row to come back?

Strategy

Before solving these harder problems, let's try finding how many rows before 2 in the top row or 3 in the top row come back.

• Two in the top row means we count by 2s and 3s.
• Three in the top row means we count by 2s, 3s and 4s.

The answer is in the last picture above!

The NRICH web site has a neat, software-based extension of this activity which they call Poly Plug Pattern.