# Problem of the Week

**Note** Many of the math problems on this page can be found in my new book: The Green-Eyed Dragons and Other Mathematical Monsters.

I posted a problem here, each week from 2002 to 2004. Some problems are new, and some are classics. Half of them are physics (the odd weeks), and half are math (the even weeks). In most cases they're quite difficult. After all, I call them "Problems of the Week," and not "Problems of the Hour"!

Many of the physics problems can be found scattered throughout the textbook (the red book on this page) for the Physics 16 course here at Harvard.

- David Morin

 Week 90 (5/31/04) Problem90 (The game of NIM) Solution90 Week 89 (5/24/04) Problem89 (Rope between inclines) Solution89 Week 88 (5/17/04) Problem88 (Ladder envelope) Solution88 Week 87 (5/10/04) Problem87 (Leaving the hemisphere) Solution87 Week 86 (5/3/04) Problem86 (Shifted intervals) Solution86 Week 85 (4/26/04) Problem85 (Tower of cylinders) Solution85 Week 84 (4/19/04) Problem84 (Poisson and Gaussian) Solution84 Week 83 (4/12/04) Problem83 (The brachistochrone) Solution83 Week 82 (4/5/04) Problem82 (Standing in a line) Solution82 Week 81 (3/29/04) Problem81 (Rainbows) Solution81 Week 80 (3/22/04) Problem80 (Nine divisible by 9) Solution80 Week 79 (3/15/04) Problem79 (Propelling a car) Solution79 Week 78 (3/8/04) Problem78 (Infinite square roots) Solution78 Week 77 (3/1/04) Problem77 (Relativistic momentum paradox) Solution77 Week 76 (2/23/04) Problem76 (Crawling ant) Solution76 Week 75 (2/16/04) Problem75 (Hanging chain) Solution75 Week 74 (2/9/04) Problem74 (Comparing the numbers) Solution74 Week 73 (2/2/04) Problem73 (Chain on a scale) Solution73 Week 72 (1/26/04) Problem72 (Find the foci) Solution72 Week 71 (1/19/04) Problem71 (Maximum trajectory length) Solution71 Week 70 (1/12/04) Problem70 (Painting a funnel) Solution70 Week 69 (1/5/04) Problem69 (Compton scattering) Solution69 Week 68 (12/29/03) Problem68 (Tower of circles) Solution68 Week 67 (12/22/03) Problem67 (Inverted pendulum) Solution67 Week 66 (12/15/03) Problem66 (Bowl of spaghetti) Solution66 Week 65 (12/8/03) Problem65 (Relativistic cart) Solution65 Week 64 (12/1/03) Problem64 (Attracting bugs) Solution64 Week 63 (11/24/03) Problem63 (Minimal surface) Solution63 Week 62 (11/17/03) Problem62 (Leftover dental floss) Solution62 Week 61 (11/10/03) Problem61 (Falling rope) Solution61 Week 60 (11/3/03) Problem60 (Cereal box prizes) Solution60 Week 59 (10/27/03) Problem59 (Getting way ahead) Solution59 Week 58 (10/20/03) Problem58 (Coins and Gaussians) Solution58 Week 57 (10/13/03) Problem57 (Throwing a beach ball) Solution57 Week 56 (10/6/03) Problem56 (Stirling's formula) Solution56 Week 55 (9/29/03) Problem55 (Fixed highest point) Solution55 Week 54 (9/22/03) Problem54 (Rolling the die) Solution54 Week 53 (9/15/03) Problem53 (Circles on the ice) Solution53 Week 52 (9/8/03) Problem52 (Construct the center) Solution52 Week 51 (9/1/03) Problem51 (Accelerating spaceship) Solution51 Week 50 (8/25/03) Problem50 (Equal segments) Solution50 Week 49 (8/18/03) Problem49 (Falling chimney) Solution49 Week 48 (8/11/03) Problem48 (The hotel problem) Solution48 Week 47 (8/4/03) Problem47 (Sliding ladder) Solution47 Week 46 (7/28/03) Problem46 (The birthday problem) Solution46 Week 45 (7/21/03) Problem45 (Sliding along a plane) Solution45 Week 44 (7/14/03) Problem44 (Relatively prime numbers) Solution44 Week 43 (7/7/03) Problem43 (Infinite Atwood's machine) Solution43 Week 42 (6/30/03) Problem42 (How much change?) Solution42 Week 41 (6/23/03) Problem41 (Speedy travel) Solution41 Week 40 (6/16/03) Problem40 (Staying ahead) Solution40 Week 39 (6/9/03) Problem39 (Viewing the spokes) Solution39 Week 38 (6/2/03) Problem38 (Sum over 1) Solution38 Week 37 (5/26/03) Problem37 (Bouncing down a plane) Solution37 Week 36 (5/19/03) Problem36 (Monochromatic triangle) Solution36 Week 35 (5/12/03) Problem35 (Rising hoop) Solution35 Week 34 (5/5/03) Problem34 (Counterfeit coin) Solution34 Week 33 (4/28/03) Problem33 (Ball rolling in a cone) Solution33 Week 32 (4/21/03) Problem32 (The game show) Solution32 Week 31 (4/14/03) Problem31 (Simultaneous claps) Solution31 Week 30 (4/7/03) Problem30 (Difference of powers) Solution30 Week 29 (3/31/03) Problem29 (Balls in a semicircle) Solution29 Week 28 (3/24/03) Problem28 (Rectangle in a circle) Solution28 Week 27 (3/17/03) Problem27 (Relativistic cookies) Solution27 Week 26 (3/10/03) Problem26 (Drunken walk) Solution26 Week 25 (3/3/03) Problem25 (Maximum deflection angle) Solution25 Week 24 (2/24/03) Problem24 (Verifying weights) Solution24 Week 23 (2/17/03) Problem23 (V(x) versus a hill) Solution23 Week 22 (2/10/03) Problem22 (Trading envelopes) Solution22 Week 21 (2/3/03) Problem21 (Ball on turntable) Solution21 Week 20 (1/27/03) Problem20 (Collinear points) Solution20 Week 19 (1/20/03) Problem19 (Block and bouncing ball) Solution19 Week 18 (1/13/03) Problem18 (Distribution of primes) Solution18 Week 17 (1/6/03) Problem17 (Icosahedron of resistors) Solution17 Week 16 (12/30/02) Problem16 (Letters in envelopes) Solution16 Week 15 (12/23/02) Problem15 (Maximal gravity) Solution15 Week 14 (12/16/02) Problem14 (Find the angles) Solution14 Week 13 (12/9/02) Problem13 (Unchanged velocity) Solution13 Week 12 (12/2/02) Problem12 (Decreasing numbers) Solution12 Week 11 (11/25/02) Problem11 (Break or not break?) Solution11 Week 10 (11/18/02) Problem10 (Product of lengths) Solution10 Week 9 (11/11/02) Problem9 (Fractal moment) Solution9 Week 8 (11/4/02) Problem8 (Sub-rectangles) Solution8 Week 7 (10/28/02) Problem7 (Mountain climber) Solution7 Week 6 (10/21/02) Problem6 (Flipping a coin) Solution6 Week 5 (10/14/02) Problem5 (The raindrop) Solution5 Week 4 (10/7/02) Problem4 (Passing the spaghetti) Solution4 Week 3 (9/30/02) Problem3 (Balancing a pencil) Solution3 Week 2 (9/23/02) Problem2 (Green-eyed dragons) Solution2 Week 1 (9/16/02) Problem1 (Basketball and tennis ball) Solution1