Going Round in Circles

Stage: 3 Challenge Level:

If today is Monday, it will be Monday again in 7 days, 770 days, 140 days, 35 035 days,
14 000 000 007 days...

It will be Wednesday in 2 days, 72 days, 702 days, 772 days, 779 days, 1402 days, 51 days...

Convince yourself that all of this is true. We've chosen these numbers carefully to make it possible for you to check without needing to use a calculator! Suggest some other numbers we could have chosen.

Anita wants to know what day it will be in 1000 days' time.
She works out that it will be Monday in 700 days, 770 days, and 840 days... Can you suggest how Anita could continue and solve her problem?

Luke decides it might be quicker to use a calculator. He divides 1000 by 7 and gets the answer 142.8571429 on the screen. Then he multiplies 142 by 7. How does this help Luke to solve the problem?

Mathematicians are always looking for efficient ways to solve problems. Can you find efficient ways to answer some of the questions below, using mental, pencil and paper, or calculator methods?

• 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)?
• 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?

Published November 2009.

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