KA-0166●●●5 points, difficulty 3 of 35 ptLevel 9–10not yet calibratedSix friends sit around a circular table. Two seatings count as the same if one can be turned into the other by rotating the table. How many genuinely different seatings are there?CNT-15Counting up to symmetryalso CNT-16, CNT-05
KA-0167●●●5 points, difficulty 3 of 35 ptLevel 9–10not yet calibratedThe numbers 1 to 10 are written on a board. You repeatedly rub out any two of them and write down their positive difference instead, until a single number is left. What can be said about that final number?LOG-05Parity argumentsalso LOG-06, CFT-03
KA-0168●●●5 points, difficulty 3 of 35 ptLevel 9–10not yet calibratedAn ordinary six-sided die is rolled three times. What is the probability that at least one roll shows a six?CNT-09Complementary countingalso CNT-16, CFT-11