00:00 Today I only have two riddles for you, but it means that you're not going to crack them easily.
00:05 Prepared? Here's the first one.
00:07 Far, far away from any civilization, there is a remote island with 20 inhabitants.
00:14 They were born there and all their lives they've been into math, which helped them become pretty perfect logicians.
00:22 Unfortunately, they're imprisoned, being trained to win the Nobel Prize, and they can't leave the island.
00:29 Well, actually, there's a way.
00:32 Each islander can approach a guard at night and ask to leave the island.
00:37 If the islander who asked to leave has green eyes, they will be allowed to leave.
00:41 If not, they'll be tossed into the island's volcano instead.
00:45 So, obviously, no one takes the risk, because none of them knows their eye color.
00:51 The thing is that all of them actually have green eyes, so each one could theoretically leave.
00:57 But, well, none did.
01:00 They don't have any reflective surfaces, they're mute, and they're not allowed to communicate with each other in any way.
01:06 The only time they all see each other is during the lineup every morning.
01:11 One day, I got the privilege to travel to the island and present myself during the lineup.
01:16 I could make an announcement, but there was one strict rule.
01:20 I couldn't tell them any new information unless I wanted to be thrown into a volcano.
01:25 But I really wanted to help those guys out, so here's what I said.
01:30 At least one of you has green eyes.
01:33 How many days will it take all of them to leave the island after my announcement?
01:37 Okay, maybe 20 is a bit hard to figure out right away.
01:41 So let's first consider the case of two islanders, Etta and Fai.
01:46 Both of them have green eyes, but they don't know their eye color.
01:50 So the day when I announce the statement, they pay attention to it and look at each other, remembering the eye color.
01:57 Etta sees that Fai has green eyes, which aligns with my statement, but she can't be sure that she has green eyes too.
02:05 Fai does the same.
02:07 She sees Etta's green eye color, but he isn't sure about his own eye color.
02:12 So the night comes and none of them leaves.
02:16 When they both see each other the next day, they realize something.
02:20 Etta realizes that if Fai had seen that she didn't have green eyes,
02:25 he would have understood that the one person with green eyes was him and would have left the island that night.
02:31 But he didn't do it.
02:33 So Etta realizes that Fai saw her green eyes and wasn't sure about his eye color.
02:39 So her eyes must be green.
02:42 Fai has the very same logic and figures out that he has green eyes too.
02:47 So now they both know it, and the second night they both leave.
02:52 In the case of the two islanders, they both left the second night.
02:56 Now let's say there are three people on the island, Etta, Fai, and Theta.
03:01 Each of them sees two green-eyed people, but they still can't be sure about their own eye color.
03:08 So no one leaves the first night.
03:10 In the morning, they see each other again, but unfortunately, none of them are sure again.
03:16 Theta thinks that possibly her eyes aren't green and Etta and Fai were watching each other.
03:23 She figures that now they will both see that none of them left and will leave the next night.
03:29 Each one of the three thinks so, and once again, no one leaves.
03:34 The second night passes and the three islanders meet the third morning.
03:38 So Theta is now sure that Etta and Fai weren't just watching each other, but her too.
03:44 So she must have green eyes.
03:47 Etta and Fai, who were following the same logic all the way, realize the same thing.
03:53 So all of them figure that they have green eyes and leave on the third night.
03:57 Now if I add another islander, the same logic will work, and it'll take one more night to figure it out.
04:04 In our case, there are 20 islanders.
04:07 They will all see 19 green-eyed islanders and will all wonder if others see 18 or 19 green-eyed islanders.
04:16 So they will watch each other for 19 nights, and when they see each other on the 20th morning,
04:21 they will all leave on the 20th night after that.
04:25 OK, great job! Here's the second riddle.
04:28 This one is much easier in my opinion, so I'll give you a little break.
04:32 But you still need to keep your brains turned on.
04:35 You take a voyage across a sea, delivering fish tanks with rare species of fish to scientists,
04:42 who will work on increasing the population of that said fish species.
04:46 But on your way, you get into a storm, and the fish tanks get drowned in the sea.
04:51 The records get lost too, so you're not even sure how many fish tanks there were to start with.
04:57 Still, you must find them all.
05:00 Good news! There's a rescue submarine you can use, but there's only enough fuel for one trip to the bottom of the ocean.
05:07 So, before going down, you make some inspections.
05:11 Thermal imaging detects 50 organisms in the areas where you have lost the fish tanks.
05:16 Those are your fish and sharks, which are not yours.
05:20 Using a scanner, you scan three regions of the sea more closely.
05:25 Region A, Region B, and Region C.
05:28 The scanner shows that in Sector A, there are four fish tanks and two sharks.
05:33 In Region B, there are two fish tanks and four sharks.
05:37 Just as you're about to scan Region C, the scanner breaks down and doesn't show you anything.
05:43 So, you need to figure out how many fish tanks there are to send to the submarine.
05:48 This is not an easy task, especially with lost records.
05:53 You don't know exactly how many fish tanks were on board, but you remember that there were no more than 13 of them.
06:00 You also don't know how many fish there are in each fish tank, but you know that it's the same amount in each one of them.
06:08 There's also information that in every sector, there's a different amount of sharks, and not more than seven in each one of them.
06:15 Knowing all this, can you figure out how many fish tanks drowned in Sector C?
06:21 The best way to solve this kind of problem is by using a table.
06:25 So, we know that there are 13 fish tanks at most.
06:30 Six of them were located in Sectors A and B, so there are between six to 13 fish tanks in total.
06:37 Can't be more, can't be less, since we already have six.
06:42 Now, let's move on to the sharks.
06:44 In each sector, there are no more than seven sharks.
06:48 Also, there's never the same amount of sharks in two regions.
06:52 Since Regions A and B have two and four sharks, the possible number of sharks in Region C is one, three, five, six, and seven.
07:03 Let's put these numbers in the rows.
07:05 In a column next to it, we put six in each row.
07:08 That's the number of sharks in Regions A and B.
07:12 Now we know that there were 50 creatures located in the waters.
07:16 So, for each possible amount of sharks, we can calculate the remaining amount of fish.
07:22 43 in case of six sharks plus one in Region C.
07:26 41 in case of six sharks plus three in Region C.
07:31 39 in case there are five sharks in Region C.
07:35 38 if there are six sharks there.
07:38 And 37 fish in total if there are seven sharks in the last region.
07:43 Okay, now we have to remember that the number of fish is the same in every tank.
07:49 So, the total amount of fish must be divisible by one of the possible values for the total amount of fish tanks.
07:57 43, 41, and 37 are prime numbers that aren't divisible at all.
08:04 In case of 38, we'd need 19 tanks.
08:07 Two fish in each, but we know that the maximum number of fish tanks is 13.
08:13 So, the only possible scenario is 39 fish in 13 tanks, meaning three fish in each tank.
08:20 So, in Region C, seven more fish tanks got lost on the bottom of the sea.
08:26 I hope you can find them all now!
08:28 That's it for today.
08:29 So, hey, if you pacified your curiosity, then give the video a like and share it with your friends.
08:34 Or, if you want more, just click on these videos and stay on the Bright Side!
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