mathematical beginnings logo new small.png Pens in a Cup

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Learners could start with all the pens the same size (say, unit diameter) and vary the diameter of the cup, checking each time how many will fit in. Starting with a cup diameter of 1 and increasing by 1 each time, they will find the sequence 1, 2, 7, 11, 19, ... (sequence A023393 at The On-Line Encyclopedia of Integer Sequences).


Smaller pens can of course be fitted into the gaps leftover, but then it becomes much more complicated!

Colin Foster 2012,