Holiday puzzles
We at Problem of the Week would like to wish you a wonderful, very restful holiday! For those of you…
Problem of the Week (41)
Chloé chooses a real number uniformly at random from the interval . Independently, Laurent chooses a real number uniformly at random…
Problem of the Week (40)
Among the constants , there are equal to and equal to . Find the sum of all the products ,…
Problem of the Week (39)
Compute the sum of all positive integers for which the expression is an integer. Source: HMMT February 2021 (Harvard-MIT Mathematics…
Problem of the Week (38)
What is the least possible value of for all real numbers ? Source: AMC 12A 2021 Happy problem solving! Email…
Problem of the Week (37)
Leo the fox has a 5 by 5 checkerboard grid with alternating red and black squares. He fills in the…
Problem of the Week (36)
In the tribe of Zimmer, being able to hike long distances and knowing the roads through the forest are both…
Problem of the Week (35)
This an incredible problem—incredible because it seems to lack sufficient data for a solution. A cylindrical hole six inches long…
Problem of the Week (34)
The solution of the equation can be expressed in the form . Find . Source: AMC 12A 2010 Happy problem…
Problem of the Week (33)
Suppose there exists a convex (all angles less than 180 degrees) -gon (polygon with sides) such that each of its…