Enter a number and the scratch will create that many circles with a band wrapped tightly around it. It is curved on the corners, but straight in between circles. It can go pretty high, and eventually the circles are too small to see (after about 250.) It can lag out, too (at about 725.) Please comment numbers that do not work so I can add them to the list below.
This is the MathCounts challenge (problem #10 of the following worksheet) https://www.mathcounts.org/sites/default/files/u50/MCMini11Q.pdf For some reason, some numbers does not work (meaning either two circles overlap, don't touch, or some other reason)... 1 11 13 14 21 22 25 32 108 249 250 300 301