KA-0173●●○4 points, difficulty 2 of 34 ptLevel 11–12not yet calibratedEach of the four edges of a square is painted either black or white. Two paintings count as the same if one can be rotated onto the other. How many genuinely different paintings are there?CNT-15Counting up to symmetryalso CNT-04, LOG-11
KA-0175●●●5 points, difficulty 3 of 35 ptLevel 11–12not yet calibratedWhat is the smallest number n such that ANY collection of n whole numbers must contain two of them whose difference is divisible by 7?CNT-17The pigeonhole principlealso NUM-06, LOG-09
KA-0177●●●5 points, difficulty 3 of 35 ptLevel 11–12not yet calibratedHow many diagonals does a convex polygon with 12 sides have? A diagonal joins two vertices that are not already joined by a side.CNT-16Overcount, then correctalso CNT-06, GEO-05