Source: Mathematical Puzzles of Sam Loyd, Volume Two, edited by Martin Gardner, Dover Publications, New York, 1960, #90, #94.
To let you know I used your 2 current puzzles as the springboard for my next 2 puzzles that I'll submit next week to panthera's: PUZZLE1 Well, I've decided to lower my standards and bore you with a couple of straight math puzzles. You gotta huge floor, 1050 by 700. You paint it this way: -green strip x wide all around the outer edge -next to this, pink strip y wide -next to this, polkadot strip z wide -you're left with a rectangle at center: babyblue. Warning: start at center, else you'll be stuck there... After all's done, you measure to find the areas: -green: 3/5 of floor -pink: 1/7 of floor -polkadot: 1/10 of floor What are the "floored"(how appropriate!) values of x y z? Enter like this: x-y-z And now go to my next one; bring your paintbrush to help B paint his new bridge... PUZZLE2 A and B are standing at X on south edge of a river, 100 wide. There's a bridge on their right (east), 50 from X. There's also a bridge on their left. Both bridges 100 long. A and B leave together; A goes right, B goes left (west). B walks at twice A's speed (main reason: has longer legs). A walks the 50 to the bridge, then crosses over. A continues directly north, a distance of 50, to point P. B reaches the other bridge, then crosses over. B then walks a straight path, heading toward P. (if your B is not heading in a general "northly-eastly" direction, then you better stop and re-read the above!) When A arrives at P, B still has 50 to go before reaching P. Ok; in order to make this puzzle possible, B decides to lengthen the bridge he crossed on, making it cross the river at an angle, keeping its position on the south side the same. B does this such that in the future, when the above walkathon is similarly repeated, he gets to point P at same time as A. B punches keys on his handheld Texas Instrument EL-733-A to realise that he has 2 options, that is that he can have 2 bridges (different lenghts) to accomplish his goal.