Problem of the Week

For those of you looking for some problems and puzzles to brood over, I'll post a new problem here each week, the solution to which I'll post the following week. Some are new, and some are classics. I won't limit them to physics, so many will be of the mathematical sort. (The pattern I seem to have settled into is physics problems on the odd weeks, and math problems on 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"!

Feel free to stop by my office (Lyman 238) if you get an answer or want any hints. Have fun!

Many of the physics problems can be found scattered throughout the textbook for the Physics 16 course here at Harvard.

Well, I'm going to take a break now since I have to work on some other things. I'll pick it up again sometime down the road. But these 90 problems should keep you busy for a while!

**NEW!** If you're looking for some slightly tamer (but still challenging) mechanics problems, compared with the ones here and in the Physics-16 textbook, I've written a new problem book based on my material from the Physics-15a course at Harvard. It's the first book listed on the textbook page. It's self-published and hence super cheap -- under $15 for the paperback, and under $6 for the Kindle version.

— 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

© 2004 by David Morin