No problem is worth more than 3 minutes of your 40. If you don’t see the path in 60 seconds, circle it, move on, and return if time permits.
Permutations, combinations, and geometric probability. Mathcounts National Sprint Round Problems And Solutions
Students try to brute force. You cannot. You must use modular arithmetic and symmetry. No problem is worth more than 3 minutes of your 40
Draw rectangle ABCD with AB = 12 (horizontal), AD = 5 (vertical). Let A = (0,0), B = (12,0), C = (12,5), D = (0,5). "From one corner to the midpoint of the opposite side": Choose corner A(0,0). Opposite side is BC? No – the side opposite A is side CD. The midpoint of CD: C(12,5) to D(0,5) → midpoint M = (6,5). Distance AM = (\sqrt{(6-0)^2 + (5-0)^2} = \sqrt{36 + 25} = \sqrt{61}). So answer is (\sqrt{61}) cm. Students try to brute force