Under A simple equation (in Just Math) Posted on 2018-06-24 (3 Comments) |

| solution with proof by Paul (2018-06-25 09:50:23) |

Under Where's Bob? (in General) Posted on 2018-05-01 (4 Comments) |

| An improvement, but not a provable minimum by Paul (2018-05-01 15:04:51) |

Under Comb(k,2) (in Numbers) Posted on 2018-03-29 (4 Comments) |

| Solution with proof by Paul (2018-03-29 12:23:53) |

Under Dimsums LTD (in Numbers) Posted on 2017-10-16 (1 Comments) |

| solution by Paul (2017-10-16 10:40:41) |

Under Lots of lods (in Sequences) Posted on 2017-09-10 (7 Comments) |

| Alternate approach by Paul (2017-09-11 11:34:05) |

Under Prime ages (in Just Math) Posted on 2017-08-23 (1 Comments) |

| solution by Paul (2017-08-23 11:41:27) |

Under Commutative Exponentiation (in Just Math) Posted on 2017-07-07 (6 Comments) |

| rest of the solution by Paul (2017-07-07 15:09:38) |

| rational solutions by Paul (2017-07-07 14:53:40) |

Under The Dot-town Suicides (in Logic) Posted on 2017-04-20 (1 Comments) |

| explanation (maybe not rigorous enough for proof) by Paul (2017-04-24 10:01:33) |

Under Growth Potential (in Algorithms) Posted on 2017-04-13 (4 Comments) |

| Yet another proof by Paul (2017-04-13 12:25:16) |

Under QUICKIE X (in Just Math) Posted on 2017-03-28 (3 Comments) |

| a bit sketchy but still a solution by Paul (2017-03-29 12:23:15) |

Under At most - equality (in Just Math) Posted on 2017-03-06 (1 Comments) |

| solution by Paul (2017-03-06 08:45:57) |

Under Square expressions (in Numbers) Posted on 2017-02-18 (3 Comments) |

| re: A solution by Paul (2017-02-20 17:41:09) |

Under Sets' intersection (in Just Math) Posted on 2017-02-16 (2 Comments) |

| solution by Paul (2017-02-16 11:34:57) |

Under Age Progression (in Numbers) Posted on 2017-01-16 (3 Comments) |

| solution? by Paul (2017-01-16 12:39:18) |

Under Prime candidates (in Just Math) Posted on 2016-12-20 (5 Comments) |

| re(2): solution -@ Paul by Paul (2016-12-23 12:03:22) |

| solution by Paul (2016-12-20 13:28:38) |

Under In terzo luogo (in Sequences) Posted on 2016-11-13 (4 Comments) |

| solution by Paul (2016-11-15 09:32:48) |

Under Random Trial (in Algorithms) Posted on 2016-10-02 (3 Comments) |

| One approach by Paul (2016-10-03 12:46:40) |

Under Number prediction (in Tricks) Posted on 2016-09-26 (1 Comments) |

| suspicious by Paul (2016-09-26 16:16:09) |

Under Duodecimal Pandigital Divisibility Device (in Algorithms) Posted on 2016-09-13 (2 Comments) |

| re: Choice of two algorithms by Paul (2016-09-13 19:01:57) |

Under Divisibility Property (in Numbers) Posted on 2016-08-31 (2 Comments) |

| Without Software by Paul (2016-08-31 13:59:45) |

Under Guessing your birthdate (in Just Math) Posted on 2016-08-18 (4 Comments) |

| part a by Paul (2016-08-19 17:52:14) |

Under Divisibility with lcm and gcd (in Just Math) Posted on 2016-08-15 (4 Comments) |

| re(2): Answer and reasoning by Paul (2016-08-16 11:32:42) |

| Answer and reasoning by Paul (2016-08-15 13:30:32) |

Under Rocking moves (in Logic) Posted on 2016-05-17 (3 Comments) |

| Solution by Paul (2016-05-17 15:26:44) |

Under No Equal Weighings (in Weights and Scales) Posted on 2016-04-18 (4 Comments) |

| Analytic confirmation by Paul (2016-04-20 11:00:42) |

Under One of Sixteen (in Weights and Scales) Posted on 2015-12-29 (12 Comments) |

| Solution (hard) by Paul (2015-12-30 12:08:39) |

Under Get the right product (in Just Math) Posted on 2015-12-01 (5 Comments) |

| solution by Paul (2015-12-01 17:56:12) |

Under Four factors (in Just Math) Posted on 2015-11-06 (2 Comments) |

| solution by Paul (2015-11-06 09:48:00) |

Under Must differ by 3 (in Just Math) Posted on 2015-10-23 (3 Comments) |

| analytic solution by Paul (2015-10-27 11:19:17) |

Under Palindromes and Divisibility (in Just Math) Posted on 2015-10-16 (3 Comments) |

| analytic solution by Paul (2015-10-16 12:16:55) |

Under Black and white socks (in Probability) Posted on 2015-09-29 (8 Comments) |

| re(2): Solution?? by Paul (2015-09-29 14:31:08) |

| Solution?? by Paul (2015-09-29 11:59:43) |

Under Expression Product Exercise (in Just Math) Posted on 2015-09-18 (5 Comments) |

| Not especially rigorous but hopefully valid solution by Paul (2015-09-21 15:19:24) |

Under Some definite results (in Numbers) Posted on 2015-09-17 (5 Comments) |

| re(2): non-analytic solution by Paul (2015-09-18 10:00:19) |

| non-analytic solution by Paul (2015-09-17 14:53:14) |

Under Eight efficient blacksmiths (in Just Math) Posted on 2015-08-13 (4 Comments) |

| Solution (slightly differently) by Paul (2015-08-13 11:14:14) |

Under Red, White, and Blue (in Logic) Posted on 2015-07-29 (4 Comments) |

| proof by Paul (2015-07-29 15:47:02) |

Under Island Adventure 2 (in Liars and Knights) Posted on 2015-04-21 (4 Comments) |

| Answer with explanation by Paul (2015-04-22 19:13:20) |

Under Geometric and Harmonic Harmony (in Just Math) Posted on 2014-12-15 (4 Comments) |

| solution (no proof) by Paul (2014-12-15 16:34:06) |

Under Balancing weights (in Weights and Scales) Posted on 2014-11-06 (2 Comments) |

| solution by Paul (2014-11-06 11:50:03) |

Under 4 ways (in Sequences) Posted on 2014-06-04 (6 Comments) |

| solution by Paul (2014-06-04 18:08:56) |

Under Sequence containing itself (in Numbers) Posted on 2014-05-14 (1 Comments) |

| sketch of proof by Paul (2014-05-14 22:44:11) |

Under Increase or decrease by one (in Numbers) Posted on 2014-04-22 (2 Comments) |

| Analytic Solution by Paul (2014-04-22 18:46:22) |

Under Perfectly Harmonic (in Just Math) Posted on 2013-11-13 (3 Comments) |

| Solution by Paul (2013-11-13 19:58:55) |

Under Forty-five Product (in Just Math) Posted on 2013-10-28 (2 Comments) |

| Solution a slightly different way by Paul (2013-10-28 15:14:24) |

Under What's the ... (in Just Math) Posted on 2013-06-27 (2 Comments) |

| solution? by Paul (2013-06-27 19:24:22) |

Under Infinite Product (in Numbers) Posted on 2013-06-24 (3 Comments) |

| Analytic solution by Paul (2013-06-24 18:07:53) |

Under Integer Pairs (in Just Math) Posted on 2013-05-30 (2 Comments) |

| solution with very inelegant proof by Paul (2013-06-04 03:11:16) |

Under Generalize (in Numbers) Posted on 2013-05-01 (5 Comments) |

| re: Can you prove it? by Paul (2013-05-02 15:13:03) |

Under Mission impossible (in Just Math) Posted on 2013-04-03 (5 Comments) |

| Solution a different way by Paul (2013-04-03 19:31:05) |

Under Covert Quantity (in Logic) Posted on 2013-04-02 (4 Comments) |

| Solution with proof by Paul (2013-04-03 19:44:04) |

Under Slope products (in Geometry) Posted on 2011-11-08 (3 Comments) |

| Solution by Paul (2011-11-08 18:56:41) |

Under Prime Test (1) (in Numbers) Posted on 2011-04-25 (1 Comments) |

| solution by Paul (2011-04-25 20:29:17) |

Under Scarce primes (in Numbers) Posted on 2011-01-10 (10 Comments) |

| proof by Paul (2011-01-10 22:23:15) |

Under Card Tableau in Black and White (in Logic) Posted on 2010-11-30 (3 Comments) |

| complete solution by Paul (2010-11-30 22:50:57) |

Under Face book (in Cryptography) Posted on 2010-11-29 (11 Comments) |

| re(2): Applying it by Paul (2010-12-01 18:04:53) |

Under 2008 a fourth power? Baseless! (in Just Math) Posted on 2010-10-09 (3 Comments) |

| solution by Paul (2010-10-09 17:54:53) |

Under The Rebel IV (in Liars and Knights) Posted on 2010-01-30 (3 Comments) |

| solution with explanation by Paul (2010-02-02 02:57:52) |

Under Runners on a Square Field (in Just Math) Posted on 2009-01-15 (4 Comments) |

| solution by Paul (2009-01-15 22:23:20) |

Under Bulbs and Switches (in Logic) Posted on 2009-01-11 (8 Comments) |

| re(2): solution? by Paul (2009-01-15 22:24:25) |

| solution? by Paul (2009-01-12 19:05:12) |

Under Digits 251 in sequence (in Just Math) Posted on 2009-01-05 (5 Comments) |

| upper bound by Paul (2009-01-05 15:10:46) |

Under 2000 cards (in General) Posted on 2009-01-04 (9 Comments) |

| non-computer solution by Paul (2009-01-05 17:39:13) |

Under Getting Squared With Dates (in Numbers) Posted on 2008-12-23 (3 Comments) |

| (mostly) non computer-assisted solution by Paul (2008-12-23 18:12:51) |

Under Going Digital With Pythagoras (in Just Math) Posted on 2008-11-08 (3 Comments) |

| analytic solution by Paul (2008-11-08 23:38:36) |

Under Two Polygons (in Numbers) Posted on 2008-10-29 (5 Comments) |

| re: solution by Paul (2008-10-29 15:36:43) |

Under Pretty Potent Power Pair(s) (in Just Math) Posted on 2008-10-22 (2 Comments) |

| solution by Paul (2008-10-22 18:59:53) |

Under Cows, horses and dogs (in Just Math) Posted on 2008-10-20 (12 Comments) |

| proof of uniqueness by Paul (2008-10-20 21:01:56) |

Under Absolute Value And Real Constant (in Just Math) Posted on 2008-10-17 (3 Comments) |

| solution by Paul (2008-10-17 15:05:55) |

Under Crazy math? (in General) Posted on 2008-10-10 (5 Comments) |

| re(2): answer with explanation.... nice work, but by Paul (2008-10-13 05:25:14) |

| answer with explanation by Paul (2008-10-10 21:50:29) |

Under Getting Floored With 28 (in Just Math) Posted on 2008-09-06 (4 Comments) |

| Similar but not identical solution by Paul (2008-09-06 22:31:54) |

Under Doubles on reverse (in Just Math) Posted on 2008-09-02 (3 Comments) |

| Analytic solution by Paul (2008-09-02 23:12:54) |

Under Same Degree Vertices (in Logic) Posted on 2008-08-21 (1 Comments) |

| solution by Paul (2008-08-22 22:07:58) |

Under 'Snake-Eyes ' Joe (in Probability) Posted on 2008-07-28 (13 Comments) |

| possible theory by Paul (2008-07-28 19:36:45) |

Under Identify the cities (in General) Posted on 2008-07-25 (9 Comments) |

| a similar approach by Paul (2008-07-25 23:06:51) |

Under Find the Strategy (in Logic) Posted on 2008-07-02 (15 Comments) |

| Possible solution by Paul (2008-07-03 20:22:22) |

Under Perfect Square Too (in Just Math) Posted on 2008-06-21 (6 Comments) |

| solution with proof by Paul (2008-06-23 18:23:01) |

Under Devious Kinder Blocks (in Tricks) Posted on 2008-06-18 (7 Comments) |

| where's the trick? by Paul (2008-06-18 18:36:23) |

Under Evaluate this infinite product (in Calculus) Posted on 2008-06-05 (5 Comments) |

| Identity of numeric value by Paul (2008-06-06 16:03:28) |

Under Two Digit Number (in Liars and Knights) Posted on 2008-05-30 (4 Comments) |

| solution by Paul (2008-05-30 16:32:47) |

Under What a difference two roots make ! (in Calculus) Posted on 2008-05-24 (5 Comments) |

| a different approach to the same solution by Paul (2008-05-25 20:17:07) |

Under Subsquares (in Numbers) Posted on 2008-05-21 (9 Comments) |

| four by four and on by Paul (2008-05-21 21:20:42) |

| two by two by Paul (2008-05-21 20:50:41) |

Under Rooting For The Limit (in Calculus) Posted on 2008-04-23 (6 Comments) |

| not very rigorous solution by Paul (2008-04-25 23:59:00) |

Under Sum of Powers (in Numbers) Posted on 2008-04-21 (5 Comments) |

| thoughts by Paul (2008-04-24 07:38:36) |

Under Broken Lights Out (in Logic) Posted on 2008-04-07 (4 Comments) |

| towards a solution (but not quite there) by Paul (2008-04-15 04:44:22) |

Under Real Powerful Logarithms (in Just Math) Posted on 2008-04-04 (4 Comments) |

| analytic solution by Paul (2008-04-15 04:25:57) |

Under Knave Contest (in Liars and Knights) Posted on 2008-04-03 (7 Comments) |

| non-computer explanation of solution by Paul (2008-04-04 01:02:19) |

Under Dao Juxing (The way of the rectangle) (in Shapes) Posted on 2008-03-28 (6 Comments) |

| A similar conclusion by Paul (2008-03-28 20:01:28) |

Under Going Geometric With The Limit (in Calculus) Posted on 2008-03-26 (6 Comments) |

| not 100% rigorous solution by Paul (2008-03-27 02:56:37) |

Under Election in Logistan (in Liars and Knights) Posted on 2008-03-24 (31 Comments) |

| another thought by Paul (2008-03-24 17:38:34) |

Under Circular Balance (in Weights and Scales) Posted on 2008-03-20 (22 Comments) |

| equilibrium? (amendement to solution) by Paul (2008-03-27 02:35:45) |

| Equilibrium/extended solution by Paul (2008-03-21 19:50:59) |

Under Getting Primed With Subtraction And Addition (in Just Math) Posted on 2007-12-26 (5 Comments) |

| solution slightly differently by Paul (2007-12-27 21:05:57) |

Under Arrange with 3-4-5 difference (in Just Math) Posted on 2007-10-16 (7 Comments) |

| solution by Paul (2007-10-16 20:33:58) |

Under A real p puzzle (in Just Math) Posted on 2007-10-02 (5 Comments) |

| solution slightly differently by Paul (2007-10-04 06:08:22) |

Under TGIF (in Logic) Posted on 2007-08-31 (5 Comments) |

| solution by Paul (2007-09-01 19:37:24) |

Under The Last Three Digits (in Numbers) Posted on 2007-08-28 (8 Comments) |

| proof of solution by Paul (2007-08-28 19:41:59) |

Under Getting Primes With 2 And 4 (in Numbers) Posted on 2007-08-19 (6 Comments) |

| re(2): f and g by Paul (2007-08-22 17:55:30) |

| f and g by Paul (2007-08-21 15:56:52) |

Under Starbucks! (in Just Math) Posted on 2007-08-18 (11 Comments) |

| solution by Paul (2007-08-18 17:44:27) |

Under Quadruple Agent (in Probability) Posted on 2007-07-25 (11 Comments) |

| solution a different way by Paul (2007-07-26 19:29:41) |

Under Close to Fermat (in Numbers) Posted on 2007-04-06 (4 Comments) |

| inelegant solution by Paul (2007-04-07 03:40:34) |

Under Wolf in a field (in Algorithms) Posted on 2006-02-23 (17 Comments) |

| dead dog? by Paul (2006-02-25 00:02:40) |

Under Making poverty history (in Numbers) Posted on 2006-02-19 (9 Comments) |

| non-computer solution by Paul (2006-02-24 00:36:31) |

Under Challenging Chess Championship (in Games) Posted on 2005-11-16 (13 Comments) |

| starting at the bottom by Paul (2005-11-17 02:34:14) |

Under The 3-digit Number (in Just Math) Posted on 2005-10-16 (18 Comments) |

| re(3): 3 digit number by Paul (2005-10-17 23:05:36) |

Under Shorten and halve (in Word Problems) Posted on 2005-09-21 (32 Comments) |

| literal? by Paul (2005-10-01 06:46:00) |

Under A Three Way Scale (in Weights and Scales) Posted on 2005-09-05 (3 Comments) |

| a lengthy solution by Paul (2005-09-06 02:26:36) |

Under Sorta pythagoric... (in Numbers) Posted on 2005-09-01 (16 Comments) |

| re: Am I missing something? by Paul (2005-09-06 01:47:41) |

| more chipping by Paul (2005-09-05 10:09:06) |

| chipping away at the possibilities by Paul (2005-09-02 04:13:26) |

| uninteresting solution by Paul (2005-09-01 17:15:58) |

Under 7 sounds (in Word Problems) Posted on 2005-08-24 (10 Comments) |

| re: More than 7 (okay only 7) by Paul (2005-08-24 08:46:00) |

Under Digital sum (in Just Math) Posted on 2005-08-20 (7 Comments) |

| Suspicions confirmed by Paul (2005-08-20 20:32:01) |

Under Just Jauntily Jousting (in Liars and Knights) Posted on 2005-08-15 (8 Comments) |

| re(2): Ignorance is key - help! by Paul (2005-08-16 04:31:05) |

| Ignorance is key by Paul (2005-08-16 03:15:14) |

Under Where is the White King? (in Games) Posted on 2005-08-05 (21 Comments) |

| re(3): Observations -- and a hint by Paul (2005-08-05 22:02:19) |

Under Knot or Not? (in Probability) Posted on 2005-08-04 (16 Comments) |

| re: As I figure it by Paul (2005-08-04 02:28:04) |

Under Et Tu, Brute? (in Sequences) Posted on 2005-08-02 (15 Comments) |

| A more Cesarean solution by Paul (2005-08-06 01:01:27) |

Under Two to the Tee (in Numbers) Posted on 2005-07-29 (5 Comments) |

| the rest of the solution by Paul (2005-07-30 08:39:10) |

| another small observation by Paul (2005-07-29 21:13:27) |

Under Two rights out of 24 wrongs (in General) Posted on 2005-07-27 (11 Comments) |

| re: Comparing proofs by Paul (2005-07-29 21:25:42) |

| Solution by Paul (2005-07-27 00:54:49) |

Under Lemonade (in Weights and Scales) Posted on 2005-07-26 (18 Comments) |

| Solution, but not necessarily minimal by Paul (2005-07-26 02:17:51) |

Under What's Going On? (in Numbers) Posted on 2005-07-05 (4 Comments) |

| a thought by Paul (2005-07-05 21:13:22) |

Under Three Tests, Take Three! (in Weights and Scales) Posted on 2005-06-23 (14 Comments) |

| re: The answer is ... by Paul (2005-06-24 01:38:26) |

Under Even, or Odd? (in Sequences) Posted on 2005-06-20 (14 Comments) |

| re: Spoiler by Paul (2005-06-20 22:04:20) |

Under Splitting Heirs (in Shapes) Posted on 2005-06-15 (10 Comments) |

| maximum size of possible solution by Paul (2005-06-15 20:55:34) |

Under Square pairs (in Just Math) Posted on 2005-06-15 (7 Comments) |

| proof that previous solution is minimal by Paul (2005-06-15 21:09:10) |

Under Unusual binary representation (in Numbers) Posted on 2005-06-14 (9 Comments) |

| a slightly different proof by Paul (2005-06-18 01:46:25) |

Under Strange divisibility (in Just Math) Posted on 2005-05-25 (27 Comments) |

| solution by Paul (2005-06-13 21:47:24) |