0:00:07.234,0:00:10.094 As a wildfire rages through[br]the grasslands, 0:00:10.094,0:00:14.595 three lions and three wildebeest[br]flee for their lives. 0:00:14.595,0:00:16.125 To escape the inferno, 0:00:16.125,0:00:21.224 the must cross over to the left bank[br]of a crocodile-infested river. 0:00:21.224,0:00:24.310 Fortunately, there happens[br]to be a raft nearby. 0:00:24.310,0:00:27.488 It can carry up to two animals at a time, 0:00:27.488,0:00:30.995 and needs as least one lion[br]or wildebeest on board 0:00:30.995,0:00:33.351 to row it across the river. 0:00:33.351,0:00:35.674 There's just one problem. 0:00:35.674,0:00:39.806 If the lions every outnumber the[br]wildebeest on either side of the river, 0:00:39.806,0:00:41.444 even for a moment, 0:00:41.444,0:00:45.426 their instincts will kick in,[br]and the results won't be pretty. 0:00:45.426,0:00:50.075 That includes the animals in the boat[br]when its on a given side of the river. 0:00:50.075,0:00:54.255 What's the fast way for all six animals[br]to get across 0:00:54.255,0:00:57.974 without the lions stopping for dinner? 0:00:57.974,0:01:01.555 Pause here if you want [br]to figure it out for yourself. 0:01:01.555,0:01:02.815 Answer in: 3 0:01:02.815,0:01:03.845 Answer in: 2 0:01:03.845,0:01:04.796 Answer in: 1 0:01:04.796,0:01:06.911 If you feel stuck on a problem like this, 0:01:06.911,0:01:10.816 try listing all the decisions you can make[br]at each point, 0:01:10.816,0:01:14.195 and the consequences each choice[br]leads to. 0:01:14.195,0:01:18.006 For instance, there are five options[br]for who goes across first: 0:01:18.006,0:01:19.186 one wildebeest 0:01:19.186,0:01:20.186 one lion. 0:01:20.186,0:01:21.286 two wildebeest, 0:01:21.286,0:01:22.275 two lions, 0:01:22.275,0:01:23.736 or one of each. 0:01:23.736,0:01:25.245 If one animal goes alone, 0:01:25.245,0:01:27.587 it will just have to come straight back. 0:01:27.587,0:01:29.475 And if two wildebeest cross first, 0:01:29.475,0:01:32.456 the remaining one will immediately[br]get eaten. 0:01:32.456,0:01:34.976 So those options are all out. 0:01:34.976,0:01:36.597 Sending two lions, 0:01:36.597,0:01:38.267 or one of each animal, 0:01:38.267,0:01:42.506 can actually both lead to solutions[br]in the same number of moves. 0:01:42.506,0:01:45.672 For the sake of time,[br]we'll focus on the second one. 0:01:45.672,0:01:47.637 One of each animal crosses. 0:01:47.637,0:01:51.082 Now, if the wildebeest stays [br]and the lion returns, 0:01:51.082,0:01:53.537 there will be three lions[br]on the right bank. 0:01:53.537,0:01:56.457 Bad news for the two remaining wildebeest. 0:01:56.457,0:01:59.250 So we need to have the lion[br]stay on the left bank 0:01:59.250,0:02:01.939 and the wildebeest go back to the right. 0:02:01.939,0:02:03.987 Now we have the same five options, 0:02:03.987,0:02:07.137 but with one lion [br]already on the left bank. 0:02:07.137,0:02:10.298 If two wildebeest go,[br]the one that stays will get eaten, 0:02:10.298,0:02:12.417 and if one of each animal goes, 0:02:12.417,0:02:14.977 the wildebeest on the raft[br]will be outnumbered 0:02:14.977,0:02:17.728 as soon as it reached the otherside. 0:02:17.728,0:02:19.078 So that's a dead end, 0:02:19.078,0:02:20.978 which means that at the third crossing, 0:02:20.978,0:02:23.646 only the two lions can go. 0:02:23.646,0:02:25.067 One gets dropped off, 0:02:25.067,0:02:27.457 leaving two lions on the left bank. 0:02:27.457,0:02:30.457 The third lion takes the raft back to[br]the right bank 0:02:30.457,0:02:33.018 where the wildebeest are waiting. 0:02:33.018,0:02:34.238 What now? 0:02:34.238,0:02:37.297 Well, since we've got two lions waiting[br]on the left bank, 0:02:37.297,0:02:40.877 the only option is for two wildebeest[br]to cross. 0:02:40.877,0:02:44.767 Next, there's no sense in two wildebeest[br]going back, 0:02:44.767,0:02:47.339 since that just reverses the last step. 0:02:47.339,0:02:48.909 And if two lions go back, 0:02:48.909,0:02:51.919 they'll outnumber the wildebeest[br]on the right bank. 0:02:51.919,0:02:55.748 So one lion and one wildebeest[br]take the raft back 0:02:55.748,0:02:58.800 leaving us with one of each animal[br]on the left bank 0:02:58.800,0:03:00.959 and two of each on the right. 0:03:00.959,0:03:05.149 Again, there's no point in sending [br]the lion-wildebeest pair back, 0:03:05.149,0:03:07.981 so the next trip should be either[br]a pair of lions 0:03:07.981,0:03:10.098 or a pair of wildebeest. 0:03:10.098,0:03:13.889 If the lions go, they'd eat the wildebeest[br]on the left, so they stay, 0:03:13.889,0:03:16.760 and the two wildebeest cross instead. 0:03:16.760,0:03:20.840 Now we're quite close because the[br]wildebeest are all where they need to be 0:03:20.840,0:03:22.770 with safety in numbers. 0:03:22.770,0:03:25.677 All that's left is for that one lion[br]to raft back 0:03:25.677,0:03:29.390 and bring his fellow lions over[br]one by one. 0:03:29.390,0:03:31.589 That makes eleven trips total, 0:03:31.589,0:03:35.460 the smallest number needed[br]to get everyone across safely. 0:03:35.460,0:03:40.062 The solution that involves sending both[br]lions on the first step works similarly, 0:03:40.062,0:03:43.619 and also takes eleven crossings. 0:03:43.619,0:03:47.331 The six animals escape unharmed[br]from the fire just in time 0:03:47.331,0:03:50.249 and begin their new lives [br]across the river. 0:03:50.249,0:03:52.679 Of course, now that the danger's passed, 0:03:52.679,0:03:57.121 it remains to be see how long their[br]unlikely alliance will last.