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-0176●●●5 points, difficulty 3 of 35 ptLevel 11–12not yet calibratedAn 8 by 8 chessboard has two opposite corner squares removed, leaving 62 squares. Each domino covers exactly two squares that share an edge. Can the 62 squares be covered exactly by 31 dominoes?LOG-07Coloring argumentsalso LOG-09, CNT-15
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