1 00:00:00,000 --> 00:00:02,112 2 00:00:02,112 --> 00:00:04,570 SPEAKER 1: All right, let's have a look at non-threatening. 3 00:00:04,570 --> 00:00:07,000 So non-threatening we are given a chessboard 4 00:00:07,000 --> 00:00:10,270 with a bunch of letters on it and several pieces already placed 5 00:00:10,270 --> 00:00:13,210 on the board, one queen and the eight ponds. 6 00:00:13,210 --> 00:00:17,180 And we have these seven pieces remaining indicated at the bottom there. 7 00:00:17,180 --> 00:00:20,890 And apparently our goal is to find a way to safely place all of the pieces, 8 00:00:20,890 --> 00:00:23,720 so that none of them are quote, unquote threatened, 9 00:00:23,720 --> 00:00:26,884 which means basically they're subject to attack by that piece based 10 00:00:26,884 --> 00:00:27,800 on the rules of chess. 11 00:00:27,800 --> 00:00:31,082 Now of course, all the pieces in this are white. 12 00:00:31,082 --> 00:00:33,040 There's not actually two opponents going on, so 13 00:00:33,040 --> 00:00:36,109 think of this more of like a civil war where the pieces are possibly 14 00:00:36,109 --> 00:00:38,650 going to be able to attack each other even though they're all 15 00:00:38,650 --> 00:00:40,559 on the same side. 16 00:00:40,559 --> 00:00:43,600 So the first thing that you might want to do in this puzzle is figure out 17 00:00:43,600 --> 00:00:48,850 where pieces cannot possibly go based on the chess pieces that are already 18 00:00:48,850 --> 00:00:49,810 placed on the board. 19 00:00:49,810 --> 00:00:52,120 Because by placing them in any of those spaces, 20 00:00:52,120 --> 00:00:56,170 they would already be threatened or subject to attack by some other piece. 21 00:00:56,170 --> 00:01:00,460 So for example, Queens as you may know are the most powerful piece in chess. 22 00:01:00,460 --> 00:01:03,490 They can move any number of spaces in any direction, which 23 00:01:03,490 --> 00:01:07,390 means putting pieces in any of these squares 24 00:01:07,390 --> 00:01:10,360 would immediately put them under threat, because the queen could 25 00:01:10,360 --> 00:01:15,860 move to any of those squares freely and could attack any piece in any of them. 26 00:01:15,860 --> 00:01:18,650 So we can rule all of those out. 27 00:01:18,650 --> 00:01:24,160 Additionally, pawns, the pawns can only generally move forward in chess. 28 00:01:24,160 --> 00:01:27,130 They attack diagonally forward, which is, kind of, 29 00:01:27,130 --> 00:01:28,900 a strange quirk of that piece. 30 00:01:28,900 --> 00:01:32,026 And so we can also eliminate any of the two squares, or some of these pawns 31 00:01:32,026 --> 00:01:35,233 are right on the edge of the board so we might not be able to eliminate them. 32 00:01:35,233 --> 00:01:37,510 But any of the two squares diagonally in front 33 00:01:37,510 --> 00:01:43,111 of any of the pawns, which means we can also eliminate any of these squares 34 00:01:43,111 --> 00:01:43,610 as well. 35 00:01:43,610 --> 00:01:46,420 So we know right out the gate that we can't possibly 36 00:01:46,420 --> 00:01:50,020 put pieces in any of those spaces. 37 00:01:50,020 --> 00:01:51,380 So where to go from here. 38 00:01:51,380 --> 00:01:55,245 Well, this is really going to be a game of trial and error and logic. 39 00:01:55,245 --> 00:01:57,370 And there are so many ways to approach solving this 40 00:01:57,370 --> 00:01:58,840 that we're actually just going to, kind of, generally 41 00:01:58,840 --> 00:02:01,090 go over some strategies to approach this, 42 00:02:01,090 --> 00:02:03,860 and then we'll just kind of hone in on the answer. 43 00:02:03,860 --> 00:02:06,580 So for example, the easiest ones to probably figure out 44 00:02:06,580 --> 00:02:10,090 are the rooks, which are these two pieces here. 45 00:02:10,090 --> 00:02:12,862 Rooks, as you may know, can attack similar to the queen, 46 00:02:12,862 --> 00:02:14,070 but they can't go diagonally. 47 00:02:14,070 --> 00:02:18,520 So they can move up and down or left and right any number of positions. 48 00:02:18,520 --> 00:02:22,780 Now if we look at the rows and columns on the board that currently 49 00:02:22,780 --> 00:02:30,220 have no other piece in them, that really only leaves four possible spots 50 00:02:30,220 --> 00:02:32,290 for these rooks to go. 51 00:02:32,290 --> 00:02:36,350 And really they actually have to exist in either of these pairs, 52 00:02:36,350 --> 00:02:38,795 either the t and the s or the w and the e. 53 00:02:38,795 --> 00:02:41,920 Because, otherwise, then if we put them in the same column or the same row, 54 00:02:41,920 --> 00:02:45,576 they could attack each other, which would make them no longer-- 55 00:02:45,576 --> 00:02:46,450 they'd be threatened. 56 00:02:46,450 --> 00:02:48,250 So they wouldn't be non-threatened. 57 00:02:48,250 --> 00:02:50,500 So we know that the rook's have to go there 58 00:02:50,500 --> 00:02:52,780 for sure in one-- in some of those squares, which 59 00:02:52,780 --> 00:02:55,570 allows us to actually eliminate all of these squares 60 00:02:55,570 --> 00:02:57,310 as well as possible locations. 61 00:02:57,310 --> 00:03:00,790 Because regardless, there's going to be one rook in one of those columns, 62 00:03:00,790 --> 00:03:04,300 one rook in the other, and similarly one room in one of those rows, 63 00:03:04,300 --> 00:03:05,770 one rook in the other. 64 00:03:05,770 --> 00:03:08,980 So that omits all of those other squares as well. 65 00:03:08,980 --> 00:03:13,120 From here you just, kind of, need to figure out where other pieces could go. 66 00:03:13,120 --> 00:03:17,020 So for example, if we take a look at the bishops here, 67 00:03:17,020 --> 00:03:19,990 bishops are like rook's except they only attack diagonally. 68 00:03:19,990 --> 00:03:24,190 So they can go as many pieces as they want, but only along a diagonal. 69 00:03:24,190 --> 00:03:27,170 And if you take a look at what's left on the board, 70 00:03:27,170 --> 00:03:30,490 these are the only places that rook's could go. 71 00:03:30,490 --> 00:03:31,865 The night's attack in an L-shape. 72 00:03:31,865 --> 00:03:34,156 I don't have them on the slides here, but similarly you 73 00:03:34,156 --> 00:03:35,920 could figure out where they could possibly 74 00:03:35,920 --> 00:03:40,870 go to not end up in a red square and not capture some other piece. 75 00:03:40,870 --> 00:03:44,260 And the king is similar to the queen, except it can only 76 00:03:44,260 --> 00:03:47,470 go one square around where it is, but can attack in any direction. 77 00:03:47,470 --> 00:03:52,120 So based on that information, applying some logic and some practice 78 00:03:52,120 --> 00:03:56,260 and just guessing, you can figure out that ultimately the pieces that-- well, 79 00:03:56,260 --> 00:03:59,930 the places where we want to put the pieces are here. 80 00:03:59,930 --> 00:04:03,850 And if we do that now, all 16 pieces from the white side 81 00:04:03,850 --> 00:04:06,026 are not threatening each other. 82 00:04:06,026 --> 00:04:08,650 And if we look at the letters that are underneath those squares 83 00:04:08,650 --> 00:04:14,020 and read those again from left to right, top to bottom, we get the word welcome. 84 00:04:14,020 --> 00:04:16,470 And that was the answer to non-threatening.