Can you solve the cheating royal riddle? - Dan Katz
-
0:08 - 0:11You’re the chief advisor
to an eccentric king -
0:11 - 0:13who needs to declare his successor.
-
0:13 - 0:16He wants his heir to be good
at arithmetic, lucky, -
0:16 - 0:19and above all else, honest.
-
0:19 - 0:23So he’s devised a competition
to test his children, -
0:23 - 0:26and ordered you to choose the winner.
-
0:26 - 0:30Each potential heir will be given
the same two six-sided dice. -
0:30 - 0:36The red die has the numbers
2, 7, 7, 12, 12, and 17. -
0:36 - 0:42The blue one has
3, 8, 8, 13, 13, and 18. -
0:42 - 0:47The dice are fair, so each side
is equally likely to come up. -
0:47 - 0:50Each contestant will be sent
into a Royal Rolling Room, -
0:50 - 0:54where they’ll roll both dice
20 times. -
0:54 - 0:57A contestant’s score starts at zero,
and each turn, -
0:57 - 1:01they should add the total
of the two numbers rolled to their score. -
1:01 - 1:05After 20 turns, they should report
their final score. -
1:05 - 1:09The rooms are secure,
and no one observes the rolls. -
1:09 - 1:15That means a contestant could
add incorrectly, or worse, be dishonest -
1:15 - 1:18and make up a score they didn’t achieve.
-
1:18 - 1:20This is where you come in.
-
1:20 - 1:25The king has instructed you that
if you’re at least 90% sure a contestant -
1:25 - 1:29mis-added or cheated,
you should disqualify them. -
1:29 - 1:34The highest-scoring player who remains
will be the new heir to the throne. -
1:34 - 1:38After you explain the rules,
the children run to their rooms. -
1:38 - 1:43When they return,
Alexa announces her score is 385. -
1:43 - 1:52Bertram says 840. Cassandra reports 700.
And Draco declares 423. -
1:52 - 1:55The future of the kingdom
is in your hands. -
1:55 - 1:58Whom do you proclaim
to be the worthiest successor? -
1:59 - 2:05Pause now to figure it out for yourself.
-
2:06 - 2:10Upon inspection,
most of these scores are concerning. -
2:10 - 2:12Let’s start with the highest.
-
2:12 - 2:14Bertram scored 840.
-
2:14 - 2:17That’s impressive…
but is it even possible? -
2:17 - 2:21The highest numbers on the two dice
are 17 and 18. -
2:21 - 2:2617 plus 18 is 35, so in 20 rolls,
-
2:26 - 2:32the greatest possible total
is 20 times 35, or 700. -
2:32 - 2:35Even if Bertram rolled
all the highest numbers, -
2:35 - 2:38he couldn’t have scored 840.
-
2:38 - 2:40So he’s disqualified.
-
2:40 - 2:43Cassandra, the next-highest roller,
reported 700. -
2:43 - 2:48That’s theoretically possible…
but how hard is it to be that lucky? -
2:48 - 2:50In order to get 700,
-
2:50 - 2:54Cassandra would have to roll
the highest number out of six -
2:54 - 2:57on 40 separate occasions.
-
2:57 - 3:02The probability of this is 1 over 6
to the 40th power, -
3:02 - 3:09or 1 in about 13 nonillion—
that’s 13 followed by 30 zeros. -
3:09 - 3:14To put that in perspective, there are
about 7.5 billion people in the world, -
3:14 - 3:19and 7.5 billion squared
is a lot less than 13 nonillion. -
3:19 - 3:24Rolling the highest number
all 40 times is much less likely -
3:24 - 3:28than if you picked a completely random
person on Earth, -
3:28 - 3:31and it turned out
to be actor Paul Rudd… -
3:31 - 3:37and then you randomly picked again,
and got Paul Rudd again! -
3:37 - 3:42You can’t be 100% sure that Cassandra’s
score didn’t happen by chance… -
3:42 - 3:48but you can certainly be 90% sure,
so she should be disqualified. -
3:48 - 3:52Next up is Draco, with 423.
-
3:52 - 3:56This score isn’t high enough
to be suspicious. -
3:56 - 3:58But it’s impossible
for a different reason. -
3:58 - 4:01Pick a number from each die,
and add them up. -
4:01 - 4:07No matter which combination you choose,
the result ends in a 0 or a 5. -
4:07 - 4:12That’s because every red number
is 2 more than a multiple of 5, -
4:12 - 4:16and every blue number
is 3 more than a multiple of 5. -
4:16 - 4:18This means that when you add
them together, -
4:18 - 4:22you’ll always get an exact multiple of 5.
-
4:22 - 4:25And when you add rolls
that are multiples of 5, -
4:25 - 4:28the result will also be a multiple of 5.
-
4:28 - 4:32These sorts of relationships
between integers are studied -
4:32 - 4:35in a branch of math called number theory.
-
4:35 - 4:37Here number theory shows
us that Draco’s score, -
4:37 - 4:41which is not a multiple of 5,
cannot be achieved. -
4:41 - 4:44So he should be disqualified as well.
-
4:44 - 4:48This leaves Alexa,
whose score is a multiple of 5 -
4:48 - 4:50and is in the achievable range.
-
4:50 - 4:56In fact, the most likely score is 400,
so she was a little bit unlucky. -
4:56 - 5:01But with everyone else disqualified,
she’s the last heir standing. -
5:01 - 5:05All hail Queen Alexa,
the worthiest successor! -
5:05 - 5:08At least if you agree that the best way
to organize your government -
5:08 - 5:09is a roll of the dice...
- Title:
- Can you solve the cheating royal riddle? - Dan Katz
- Speaker:
- Dan Katz
- Description:
-
View full lesson: https://ed.ted.com/lessons/can-you-solve-the-cheating-royal-riddle-dan-katz
You’re the chief advisor to an eccentric king who needs to declare his successor. He wants his heir to be good at arithmetic, lucky, and above all else, honest. So he’s devised a competition to test his children, and ordered you to choose the winner. The future of the kingdom is in your hands. Can you find the worthiest successor? Dan Katz shows how.
Lesson by Dan Katz, directed by Artrake Studio.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 05:10
Alexandra Panzer approved English subtitles for Can you solve the cheating royal riddle? | ||
Alexandra Panzer accepted English subtitles for Can you solve the cheating royal riddle? | ||
lauren mcalpine edited English subtitles for Can you solve the cheating royal riddle? |