The numbers - 4, 15, 23, 24, 35 and 42 - were chosen by a machine live on television on 6 and 10 September.

A mathematician said the chance of the same six numbers coming up twice in a row was one in four million.

The lottery organisers described it as a freak coincidence and pointed out that the numbers were drawn in a different order.

TripleM wrote:
Hah, how strange.

Click here to view the secret text

×Even if there were only 42 balls, the chance would be less than 1 in 5 million. 40 or 41 would be fine rounding to the nearest million, so maybe the Bulgarian lottery doesn't have a number 13 or something strange like that..

.. or maybe the mathematician was just wrong.

Rabscuttle wrote:
I am betting that given the total number of draws in all the lotteries everywhere, it's not too surprising that something like this has come up.

a record 18 people guessed all six numbers in the 10 September draw.
Each will win 10,164 leva (£4,700).

stigant wrote:
2. Conventional wisdom is that you shouldn't pick last week's numbers because they'll never come up. This is of course theoretically (and now empirically) false as the lottery doesn't have memory meaning that any combination (including last week's numbers) is as likely to come up as any other combination. So of course, there are always the people who will play last week's numbers to make the point. Which I guess paid off, but don't they still look a little silly since they now have to split the pay 18 ways?

 WORTH
   THE
+EXTRA
------
EFFORT

Nuntar wrote:
It's impossible.

 93546   
   461
+17458
------
100354

Nuntar wrote:
If the Vizier answers "no" to your second question, he must have been born in X if he's a knight or in Y if he's a knave. Either way, you know that "no" is the correct answer to the third question, so this solution doesn't fulfil the criteria.

Nuntar wrote:
One of the characters in the book tried to use that argument There is, however, a subtle flaw in it.

(I guess it's not giving too much away if I reveal at this point that it is possible.)

jbluestein wrote:
Can it be done in one question?

Josh

DanielFishman wrote:
The argument I gave in my previous post shows that you can't get the answer in less than n questions for some previously known n.

However, take some countably infinite set of properties X, which the Vizier is known to possess (at least) one of. (And, to be pedantic, take an enumeration Y(n=1...inf) of X).

Now, for each n=1...inf, ask the Vizier:
"Are the following statements both true: 'you are a knight' and 'you do not possess property Y(n)'?"
A knave will always answer "yes" to this; a knight will answer "yes" also, unless he does possess property Y(n), in which case he will answer "no".
Then ask
"Is either of the following statements false: 'you are a knave' and 'you do not possess property Y(n)'?"
A knight will always answer "yes"; a knave will also answer "yes" if he does not possess property Y(n), but "no" if he does.

So you will keep getting answers of "yes", until you reach the first property the Vizier does have. At which point, the Vizier will answer "no" to the first question if he is a knight, and "no" to the second question if he is a knave. But because you don't know whether the Vizier has a given property or not, you will never know the correct answer to a question until he does answer "no" to a question. And because X is countably infinite and Y(n) is an enumeration of it you will eventually reach a property the Vizier does possess.

Where I'm stumped, however, is in finding a suitable set X. Age in days?

jbluestein wrote:
I think that the problem with your approach is that it requires some external form of knowledge, which the parameters of the puzzle explicitly prohibit. I can't say "Are you a knight with blond hair?", and any question about properties is essentially a variation on that theme. At least, that's the way I understand that.

Nuntar wrote:

jbluestein wrote:
I think that the problem with your approach is that it requires some external form of knowledge, which the parameters of the puzzle explicitly prohibit. I can't say "Are you a knight with blond hair?", and any question about properties is essentially a variation on that theme. At least, that's the way I understand that.

(1) The puzzle only prohibits obtaining knowledge from external sources after beginning questioning. You could ask "Are you a knight with blond hair?" since you can see his hair colour before you start.

However, you may not ask him any question to which you at that point in time know the correct answer.

Nuntar wrote:
If the Vizier answers "no" to your second question, he must have been born in X if he's a knight or in Y if he's a knave. Either way, you know that "no" is the correct answer to the third question, so this solution doesn't fulfil the criteria.

noma wrote:
But there's probably an obviousness I'm missing, so if someone could explain, I'd appreciate it. (Without the n's please. )

Nuntar wrote:
I'm not sure what you mean by "without the n's" -- that you want someone without any n's in their name, i.e. not me, to explain? Ah well, I'll give it a shot anyway.

Nuntar wrote:
The point is that the conditions of the problem prohibit you from asking question to which you, at that point (i.e. as opposed to at the beginning of your series of questions) know the correct answer.