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Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.


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Consecutive Seven

Age 11 to 14 Challenge Level:

Start with the numbers from $0$ - $20$:

numbers from 0 to 20

Can you arrange these numbers into seven sets of three numbers, so that the totals of the sets are consecutive?

For example, one set might be $\{2, 7, 16\}$

$2 + 7 + 16 = 25$

another might be $\{4, 5, 17\}$

$4 + 5 + 17 = 26$

As $25$ and $26$ are consecutive numbers these sets might be part of your solution.

Once you've found a solution, here are some questions you might like to consider:

  • Is there more than one possible set of seven consecutive totals? How do you know?
  • Is there more than one way to make the seven totals?
  • Could you make seven sets that all had the same total?
  • Could you make seven sets whose totals went up in twos? Or threes? Or...



Click here for a poster of this problem.