Rules: You can move a ball on … Lightest goes to (1L,2H), heaviest goes to (2L,1H), middle can be put to (1L,1H) of next cycle already, remaining two go to (2L,2H) [12]: Weigh (1L,2H) and (2L,1H) to identify second lightest and second heaviest, remaining 10 move to (0L,0H) in next cycle [14]: Sort four times from (0L,0H), reuse two from (1L,1H) to fill fourth weighing [18]: Determine third lightest and defer one by sorting twice from (0L,2H), two middle ones go to (1L,2H) [20]: Third heaviest and defer one by sorting twice on (2L,0H), two go to (2L,1H) [22]: Find remaining candidates for fourth lightest and heaviest by sorting (1L,1H) [23]: Determine fourth lightest and heaviest [24]: Sort three times from (0L,0H) reusing two from (1L,1H) [27]: Determine fifth lightest from (0L,2H) [28]: Determine fifth heaviest from (0L,2H) [29]: Determine sixth lightest and heaviest by sorting from (1L,2H), (1L,1H) and (2L,1H) [30]: Sort remaining 3 balls and insert in middle [31]. “This does not apply for non-rectangular puzzles and some puzzles where the edge pieces are cut interchangeably, but generally, to solve a puzzle fast, sorting is key.” These 59 brain games will guarantee your brainpower. c. Similarly Sort [(3A),(3B),(3C)] & [(3D),(3E)] and Sort (A) and (D) this will give heaviest of all. Put the weights at 4, 6 and 7 into the scale. Ball º1 is now in slot º7. Once there are only 3 balls that haven't been positively identified, a single additional test can put all 3 of these remaining balls into order. Practice these 15 habits by age 50 to save your brain at 80. Each one should be easy to justify either from scratch or by using earlier ones in the list. Pay Attention to Piece Shapes. - If you can find the lightest weight faster then the heaviest weight, then find and remove the lightest weight. According to the American Jigsaw Puzzle Society, the first puzzle was made in 1760; puzzling didn't catch on, however, until 1820. 1 2 3 4 5 6 7 8 9 A B C D E F 2+1+1 -2-> done, 3+2 -3-> done (via 2+2) We track balls on a two dimensional field of pockets: Where e.g. Still looking to find a bit more efficiency in my solution, though! Put the weights at 5, 11 and 13 into the scale. A is lighter than B… So, since E derives from an A, there are a B and a C that are heavier than E. On the other hand, E is heavier than D. Therefore, it cannot be the lightest, and there must be at least two heavier than it. $\left(\begin{array}{c}x_2\\y_2\end{array}\right)$, After all, you don’t have your hands free, and if they dislodge your ball, you are eliminated. You now have 5 ordered sets of balls. Put their heaviest balls into the box (which identifies the heaviest; and the other one is at any rate not the lightest of the remaining balls). Put the weights at 4, 9 and 14 into the scale. Do brain games actually work? “This makes it easy to simply pick out pieces to be assembled, without sorting; usually, each piece contains enough details to uniquely identify it.” Larger puzzles are a different story, however. Balls that get moved to (2L,2H) are no longer considered for any of the four positions. With a puzzle of 2,000 pieces or more, “each piece contains a much smaller portion of the full image, so it’s faster to sort into general groups,” she says. 5th Grade. Ball º1 is now in slot ºC. 24 weighings, balls found: 1, 2, 3, 4, 13, 14, 15. ! There is an algorithm that can solve this in 31 weighings. 28 weighings, balls found: 1, 2, 3, 4, 5, 11, 12, 13, 14, 15. Place the lightest and heaviest respectively in the M group.Label the middle ball from each sort as HM and LM, respectively. Remove the heaviest as W14. ! Put the lightest weight at 4 the heaviest at 7 and the other at 6. I will sometimes write things like 2+2 -2-> done where that seems clearer than putting a particular number on the right. However, we have additional information. Find the quickest method to sort all balls and glow the tube light. 6 weighings, balls found: none. We are no longer supporting IE (Internet Explorer) as we strive to provide site experiences for browsers that support new web standards and security practices. Then do the following: Put the weights at 1, 6 and 11 into the scale. What aspect of portable floating point did Java back down on? and the last of these, along with five lots of 1+1+1 -> 3, yields the claimed solution. LMN, AB, CD, HI, JK. Put the lightest weight at 1 the heaviest at 11 and the other at 6. LM, IJ, GH, EF, B, B, B, B, B. so 15 = 2*7+1 balls requires 7^2 = 49 weightings, and (for example) 2001 balls would require 1000000 weightings. Oh no! So does "lighter" mean "known not to be the heaviest" and "heavier" mean "known not to be the lightest"? HOW TO PLAY: 25 weighings, balls found: 1, 2, 3, 4, 12, 13, 14, 15. ! 5 weighings, balls found: none. Weigh the three of these that could be lightest, giving an ordered pair and two left over; weigh the three of these that could be heaviest, giving an ordered pair and one left over; weigh the remaining three. This formulas makes first all three weights equally bad (by taking the min) and then only make them better by maxing with the new value not adding since I don't know if they are different weights. Remove the lightest as W6. Put the weights at 2, 3 and 8 into the scale. “Divide the jigsaw puzzle by zones, normally identified by colors, though sometimes it can also be by textures.” For example in a puzzle about nature, “separate an area of trees and another from grass—both can be the same color but the textures are completely different.” You might be a British spy if you can complete this puzzle. (And the 3 lightest and 3 heaviest balls overall, correctly ordered.) ! Play Color Lines Puzzle Game free and compete against the best players around the world. Same way as the lightest weight, but work on $a_{00}$, $a_{10}$ and $a_{20}$ instead of $a_{00}$, $a_{01}$ and $a_{02}$, I can do better than Chelsea's and Penguino's 49 operations, as follows. Now let's rinse and repeat with the C's. 1st Grade. There may be more optimizations like that as well, it's sort of hard to keep track of what everything could be. 2nd Grade. Compare the three possibly-lightest balls (we now have an ordered triple and two left over, and have found the 6th-lightest ball). You continue this way narrowing it down from the ends until you're left with 3 balls and the final sort finishes the ordering. ! Some of that information gets lost on repeated weighings, but not all of it. I.e., ball º1 is in slot ºF, and ball ºF is in slot º1. In her personal puzzle-solving experience, “a 500 piece jigsaw is small enough to be spread out completely on a table so that all the pieces can be viewed at the same time,” McLeod shares. You enter two or three balls, press a button, and after a bit of whirring noises, the balls roll out in order by weight, heaviest first, lightest last. Of the remaining balls, those that were untested (previously "heavier") become "unknown". Weigh 3 A's, and make the new ordered set DEF. Try to sort the colored balls in the tubes until all balls with the same color stay in the same tube.