However, this now meant that Alice could play with a smaller board. She laid out a perimeter so that she was left with a board of 6 by 6 pins (as shown in the diagram). She had thought of how many elastic bands she'd need if she joined together every pair of pins that were a whole number distance apart, but that had ended up badly. So then she had another idea: join together every pair of pins that are a

*prime number*distance apart. That sounded better! Assuming, of course, that the distance between adjacent pins was a unit length.

So, how many elastic bands will Alice need this time? Do you think she'll have enough of them?!

Note, the diagram shows some examples. Also note that the bands may well overlap each other, but so long as they join two different points that's OK. For example, the horizontal line shown joining 4 pegs contains 3 rubber bands, whereas the vertical line has just 1 band.

Now, where's that Brenda? She's late!

-=0=-

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