Going Round in Circles

If you are a teacher, click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on...

Charlie said: "It's Monday today, so it will be Monday again in $7$ days..

and in $770$ days...

and in $140$ days...

and in $35 035$ days...

and in $14 000 000 007$ days!"

Alison said: "and it will be Wednesday in $2$ days...

and in $72$ days...

and in $702$ days...

and in $779$ days...

and in $14 777 002$ days!"
 

Do you agree with all of Charlie's and Alison's statements?

Charlie and Alison chose numbers that were easy to work with. Can you see why they were chosen?

Can you make up some similar statements of your own?

If today is Monday, what day will it be in $1000$ days' time?

Once you've had a go, have a look at how two students got started on this question:

Ann's Method:

Luke's Method:

Can you suggest any other methods for solving the problem?

Now try to suggest efficient methods to answer the following questions.

You could use mental strategies, pencil and paper, or calculator methods.
 

• If it is autumn now, what season will it be in $100$ seasons?
   
• If it is November, what month will it be in $1000$ months?
   
• A railway line has $27$ stations on a circular loop. If I fall asleep and travel through $312$ stations, where will I end up in relation to where I started?
   
• If it is midday now, will it be light or dark in $539$ hours?
   
• If a running track is $400$ metres around, where will I be in relation to the start after running 6 miles (approximately $9656$ metres)?
   
• I was facing North and then spun around through $945 ^\circ$ clockwise. In what direction was I facing at the end?
   
• If I get on at the bottom of a fairground wheel and the wheel turns through $5000$ degrees, whereabouts on the wheel will I be?