# Problem of the Week

Each Monday (at least for the Fall 2018 semester) a new problem will be posted.  Then on Wednesday a hint will be posted, and on Friday a solution will be posted.

## In the News

• ### Week of Dec. 10, 2018

// December 14, 2018

The Problem: Color each point of the plane red or blue. Show that there must be an equilateral triangle in the plane whose vertices are all …

• ### Week of Dec. 3, 2018

// December 7, 2018

Problem: Make the following into true equations by adding only mathematical symbols that do not involve numbers: 0 0 0 = 6   &nbs…

• ### Week of Nov. 26, 2018

// November 30, 2018

The Problem: Show that any region in the plane with area exceeding n can be translated to cover at least n + 1 points with integer coor…

• ### Week of Nov. 19, 2018

// November 23, 2018

The Problem: Assuming ‘to know’ is mutual, show that, in any gathering, there must be two people who know the same number o…

• ### Week of Nov. 12, 2018

// November 16, 2018

The Problem: Player 1 marks a corner of an nxn checkerboard and then player 2 marks a square sharing an edge with the marked square. Pl…

• ### Week of Nov. 5, 2018

// November 9, 2018

The Problem: The hour and minute hands of a clock are indistinguishable (and there is no second hand). How many moments are there in a …

• ### Week of Oct. 29, 2018

// November 2, 2018

The Problem:​ One day in the morning it started snowing at a heavy and steady rate. A snowplow started at noon and plowed 2 miles in …

• ### Week of Oct. 22, 2018

// October 26, 2018

The Problem:​ Airline passengers have purchased all assigned seats. The firstpassenger getting on the plane drops his boarding pass as he …

• ### Week of Oct. 15, 2018

// October 19, 2018

The Problem:​ A rectangular chocolate bar is made up of at least two smaller squares.Two players take turns eating a square together with …

• ### Week of Oct. 8 2018

// October 12, 2018

The Problem:​ An odd number of soldiers are stationed in a field in such a way that all the pairwise distances are distinct. Each soldier …

• ### Week of Oct. 1 2018

// October 1, 2018

The Problem:​ Find a 10 digit number whose leading digit is the number of 0’s in the number, whose next digit is the number of 1&rsq…

• ### Week of Sept. 24th 2018

// September 24, 2018

The Problem:​ 50 coins of various denominations are placed on the number line at integer positions 1 through 50. Two players alternate tak…

• ### Week of Sept. 17th 2018

// September 17, 2018

The Problem:​ Some of the squares on an nxn checkerboard are infected. A square will become infected if it shares at least two edges with …

• ### Week of Sept. 10th 2018

// September 10, 2018

The Problem: Consider the operation of multiplying any row or column of a real matrix by -1. Show that a finite number of such operatio…

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