On that AB = 'product of first six primes', A+B = composite, A-B = composite. I was unable to get any analytical insight going, but found these solutions quickly enough by hand - A=3003, B =10 or A=1365, B=22. Unfortunately, because my method was by brute force I had to check all the rest of the possibilities in order to ensure there were not still more... and THAT was a drag. Brooke Dane ------------------------------------------------------- Hi, Ed; I see there's no answer to your June 3rd puzzle: (unless you forgot to put 'em up) >A small puzzle: A B = product of first six primes. >A+B = composite. A-B = composite. What are A & B ? There are 2 solutions: A = 10, B = 3003 (3013 and 2993, both composite) A = 22, B = 1365 (1387 and 1343, both composite) In case you'd like to add a bit of challenge to June 3rd, here's a similar but more complicated one: A B C D = product of first six primes. A>B>C>D>1. X = A+B+C+D = composite. Y = A-B+C-D = composite. What are A & B & C & D ? There are 14 cases: find the 2 with same X and same Y. Answer: A B C D X Y 33 14 13 5 65 27 35 13 11 6 65 27 Denis Borris Ottawa Ontario Canada. -------------------------------------------------------- > A small puzzle: A B = product of first six primes. > A+B = composite. A-B = composite. What are A & B? Brute force search yielded 2 solutions: Solution 1: A = 1365 = 3*5*7*13 B = 22 = 2*11 A+B = 1387 = 19*72 A-B = 1343 = 17*79 Solution 2: A = 3003 = 3*7*11*13 B = 10 = 2*5 A+B = 3013 = 23*131 A-B = 2993 = 41*73 -- Stephen Kloder ----------------------------------------------------------- a = 3 * 7 * 11 * 13 = 3003 b = 2 * 5 = 10 ab = 2 * 3 * 5 * 7 * 11 * 13 a + b = 3013 = 23 * 131 a - b = 2993 = 41 * 73 -- James Deikun, Techie(tm), CSI Multimedia --------------------------------------------------- In addition to A=3003 and B=10, the only other solution to A>B, A*B=2*3*5*7*11*13, with both A+B and A-B being composite is A=1365 and B=22. (1365+22=1387=19*73 and 1365-22=1343=17*79) Al Stanger ----------------------------------------------- Ed, There are two solutions to the first six primes puzzle. A + B A - B 3013 2993 1387 1343 Dick Saunders Jr. --------------------------------------------------- If A=3003 and B=10, then (i) A*B=30030=2*3*5*7*11*13 (ii) A+B=3013=23*131 (iii) A-B=2993=41*73 Al Stanger ------------------------------------------------- S T U T T E R # I E T I E S # P E N N A S # S I N S I L # U T E N I K # S P U T A L # T E R T I S # S E M I T E # U P R I S E S I started with stammer, ?, siennas, ?, sputnik, tertial (Googled), Semites, ?. Couldn't make it work. Then tried 'stutter'. The possible intersections with other words were all, ?, SE, ?, STU, ERT, EST, all. I tried intersecting stutter/sputnik at U and the rest followed quickly. It's like some variety cryptics in that you can't write anything down until you have several answers (at least three, I think), so it needs reasonably transparent clueing. Given that, I like the idea. Acag, Treesong ---------------------------------------------------- Given this answer: R-STUTTE -PIETIES SIENNAS- TENSIL-U UTNIK-SP TIAL-TER TES-SEMI ES-UPRIS The downs are in the SAME order as the acrosses. --Philana