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Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Two Egg Timers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Quite a few students wrote in with correct solutions and two groups offered short, precise reasoning.

The first group of four: Luke, Dan, Nicholas and Luke, all from Clevedon Community School , point out that:

Any number of minutes are possible provided it is possible to time 1 minute.

While the second group of Jessica, with the help from Gemma and Tim describe, quite nicely, how to time one minute:

1 minute can be created by turning the 4 minute timer (4m) and the 7 minute timer (7m) over then as the 4m runs out you turn it over and when the 7m runs out you have one minute. Therefore, you can repeat this process x no. of times (leaving out the gaps turning the 7m over) making any number x.

Edmund, The Chinese School in Singapore; Claire, Madras College in St. Andrews; and, Jimmy, West Flegg Middle School in Great Yarmouth, also correctly solved the problem . Well done.

However, Peter wrote to us saying:

Simply repeating the one minute from end-of-T7 to the second end-of-T4 will not work as you will have to wait another $7$ minutes between the first minute and th second.

To get contiguous minutes (i.e. minutes which directly follow on from each other) you need to subtract multiples of $4$ and $7$:











The exception is $11$ where you add the two together.

Thank you for this clear solution, Peter.