Zebedees's Number

First, I want to note that you can't assume the numbers are between 1 and 5. You only know they are consecutive positive integers.

To start with, Xanthe would know Yvette's numbers at the start if her number was 1, as Yvette's number would have to be 2 (0 isn't positive). So Xanthe's number isn't 1, and the Yvette states, knowing Xanthe's number isn't 1, that she doesn't know Xanthe's number.

If Yvette's number was 1, she would know Xanthe has 2 and if Yvette's number was 2, she would know Xanthe has 3 (as Xanthe can't have 1). Which means Yvette has an other number than 1 or 2.

As Xanthe knows Yvette has an other number than 1 or 2, she must have the number 2 or 3 herself (by having 2 she would know Yvette has 3 as Yvette can't have 1, and by having 3 she would know Yvette has 4 as Yvette can't have 2).

Having 3, Yvette knows Xanthe has 2, as Xanthe couldn't have known Yvette's number if Xanthe's number was 4 (where Yvette could have 3 or 5. Having 4, Yvette knows Xanthe has 3, as Xanthe couldn't have known Yvette's number if Xanthe had 5 instead (where Ivette could have 4 or 6).

Which means, we have two possible cases:

• Xanthe has the number 2 and Yvette has the number 3 OR
• Xanthe has the number 3 and Yvette has the number 4

The conclusion is that either of the numbers must be $\boxed{3}$ .

Relevant wiki: K-level thinking

Xanthe's first statement implies that her number isn't $1$ , since that would force Yvette's number to be $2$ .

With this knowledge, Yvette still doesn't know Xanthe's number. If her number was $2$ , she would be able to conclude that Xanthe's number was three, since one of the surrounding numbers ( $1$ ) was already ruled out from the first statement. If she had a $1$ , then she would know that Xanthe must have a $2$ as well. Hence, Yvette doesn't have a $1$ or a $2$ .

Now, Xanthe does have enough information to determine Yvette's number, and we know that Yvette doesn't have a $1$ or a $2$ . This means that $1$ or $2$ must be consecutive to Xanthe's number if she were able to determine which number Yvette has.

Since we've already established that Xanthe doesn't have a $1$ , we get that Xanthe's number must be a $2$ or a $3$ , which would force Yvette to have a $3$ or a $4$ .

In both cases, $\boxed{3}$ is one of the two numbers.

Statement 1: (Xanthe) "I don't know your number."
Conclusion: Xanthe doesn't have the number 1; or else; she would directly know that Yvette has 2.

Statement 2: (Yvette) "I don't know your number."
Conclusion: Yvette doesn't have 1; or else she would have known Xanthe's number; neither does Yvette have 2; because then she could have known that Xanthe has 3; as the possibility of Xanthe having 1 was already eliminated by statement 1.

Statement 3: (Xanthe) "Now I know your number."
Conclusion: Since, Xanthe has had no other information apart from the conclusion of statement 2(i..e. Yvette doesnt have 1 or 2); this means that this information is enough for Xanthe to know Yvette's number. This means that eliminating 1 and 2 in mind leaves her with only 1 possible case; which means that Xanthe has 2 and Yvette has 3 (eliminating 1 helps Xanthe know this) or Yvette has 4 and Xanthe has 3 (eliminating 2 helps Xanthe know).

Statement 4: (Yvette) "Now I know your number."
Conclusion: Yvette must have understood what went in Xanthe's mind after her (Yvette's) previous statement (see conclusion of previous statement) and now; Yvette can easily know Xanthe's number to be 2 or 3 based on the number with her.

Note that no other case would work because then; Yvette's first statement isn't good enough for Xanthe to definitely know the other number.
Hence the two possible cases are $(2, 3); (3, 4)$ and the only number which appears in both is $\boxed {3}$

Solution: Statement 1: Xanthe doesn't know Yvette's number => Xanthe doesn't have number 1, If she would have number 1 then she would know for sure that Yvette has number 2.

Statement 2: Yvette doesn't know Xanthe's number => Yvette doesn't have number 1, If she would have number 1 then she would know for sure that Xanthe has number 2, and she also doesn't have number 2 because if she had number 2 than she would know that Xanthe has number number 3 because Xanthe doesn't have number 1 and other consecutive to 2 is 3.

Statement 3: Now Xanthe knows Yvette's number => From Statement#2, Xanthe learnt that Yvette can't have 1 or 2. So there are two cases for Xanthe to know Yvette's number. If Xanthe has 2 then she knows that Yvette must have 3 because Yvette can't have 1. If Xanthe has 3 then she knows that Yvette must have 4 because Yvette can't have 2.

Statement 4: Now Yvette knows Xanthe's number => If Yvette has number 3, then she knows that Xanthe has 2 because if Xanthe had 4, Xanthe would never know Yvette's number. If Yvette has number 4, then she knows that Xanthe has 3 becuase if Xanthe had 5 ,Xanthe would never know Yvette's number.

Now, only number which is present in both cases is 3. Hence, 3 is one of the Zebedee's numbers.

1. The first girl (X) is only sure if she has a number at either end of a known sequence (1 in the case of positive integers), then Y should have 2.
2. If not, Y is only sure if she herself has 1 or 2 (then X has either 2 or 3, correspondingly).
3. If not, X is only sure if she herself has 2 or 3.
4. If not, Y is only sure if she herself has 3 or 4. ... and so on ... N. If not, X/Y is only sure if she herself has either N-1 or N. N+1. Y/X is sure, too, as she has either N or N+1 (the phase in the picture is superfluous).

We can easily see that after every round we eliminate one number from the end of the range until one of the girls reaches either her number or the next one. Since X told she knows in the 3rd round, she has either 3 or 2. Thus Y has either 4 or 3. One of the girls surely has 3.

If Xante had any number x larger than 2, he would never know what Yvette's number is, since Yvette's number can be x+1 or x-1. No matter what Yvette says, Xante can not know Yvette's number.

When Yvette is 1, after being told that Yvette doesn't know his number, Xanthe knows Yvette's number. If Yvette was 1, he would know Xanthe's number, which would be 2, and Xanthe would know Yvette's number, since it would have to be 1 for Yvette to immediately know what Xanthe has. However, neither know the other's number in the first phase of the conversation, but they know in the second, so Yvette cannot be 1.

When Xanthe is 2, Yvette can either be 1 or 3, but since Yvette is not 1, he must be three, which is what Xanthe must have been thinking (Yvette should know my number if her's is 1, so since she doesn't know, it must be 3). It works out for Yvette, as well (Xanthe knows my number now, so she can't be 4, or she wouldn't know anything, so since Xanthe knows, she must be 2!).

X doesn't know => X > 1 (1 is the only positive integer with only 1 neighbor)

Y doesn't know => Y > 2 (as above, but 2 also has only one eligible neighbor, since X != 1)

X now knows => X = 2, Y = 3 or X = 3, Y = 4 (2 and 3 are the only integers with exactly 1 neighboring number > 2)

Therefore, 3 must be one of the numbers.

If Pearson A got number 1 or 5, she must obviously know Pearson B's number since they knew that number given is consecutive, but Pearson A does not know. Hence, Pearson A got 2,3 or 4. Now, Pearson B said she don't know Pearson A's number, hence Pearson A knew that Pearson B got 2,3 or 4. Pearson A had changed her opinion, therefore: Situation 1. if Pearson A got 2, she knew that Pearson B got 3. Situation 2. if Pearson A got 4, she knew that Pearson B got 3. [Pearson A obviously did not get number 3 because once Pearson B said she did not know, Pearson A changes her opinion.(If Pearson A get number 3, she will not change her opinion since she only know Pearson B get number 2 and 4.)]

Conclude, Pearson B get number 3.(Pearson B)

From the given options, possible answers for X and Y are:

From statement 1: For X to know Y, X must be 1 or 5. Since X don't know Y's number, then X cannot be 1 or 5. so possible X and Y are:

From statement 2: For Y to know X, Y must be 1 or 5. Since Y don't know X's number, then Y cannot be 1 or 5. so possible X and Y are:

the possible combinations of (X,Y) are: (2,3),(3,2),(3,4),(4,3) which shows that $\boxed{3}$ is always one of the numbers...
Two statements are sufficient.

For simplicity, it is obvious that the consecutive numbers over 4-5, both girls can never make sure what the other one has, and they can't have 1 either, as 0 is not allowed. The possible pair varies in 2-4, which clearly involves 3 in either of them.

To clarify further, if X has 2, she only knows Y has 1 or 3. Then when Y declares she does not know, Y obviously can't have 1. Therefore, the possible (x,y) is (2,3).

If X has 3, Y can either have 2 or 4. If Y has 2 and knows that X doesn't know her number, she can easily figure out that X can't have 1, thus knowing X will have 4. However, since Y doesn't know, X can figure out that Y doesn't have 2, thus the next possible (x,y) is (3,4).

If X has 4, Y can have either 3 or 5, but even if Y has 3, she will naturally not know X's number, for either 2,4 is still in the middle of the integers.

Thus, there are only two such possibilities, both of which confirms that either of them will have 3.

First of all we have to assume that there are only 5 numbers 1 to 5 otherwise you cant tell the answer. Now we know that both of them knows that the numbers are consecutive. When first girl says "I don't know your number". This means she don't have 1 or 5 else if she had 1 or 5 she would have knew the other number also because the two numbers are consecutive. But she still don't know the other girls number. When second girl says she too don't know the first one's number. This means she too didn't get a 1 or 5. Now both knows that the other girl didn't get a 1 or 5. Now girl 1 and 2 could have 2,3,or 4. If one has 2 or 4 then other girl has 3. Thus first one got one of the 2 or 4(as she was sure).
Thus 3 is a necessary number. But the question is vaguely posted. There is no bound on total numbers. Also 2nd girl won't be able to know the 1st girls number.

If one of them got number 1 then other can conclude the other number is 2. The only positive intger close to 1 is 2.

Both Xanthe and Yuvanthe(X and Y) got correct answer once both came to know other don't know number each other. When X=2: Y can have 2 values. 1 or 3 ( X-1 or X+1) When Y says I don't know X , X can rule out possibility of Y=1 means Y=3

When X says I don't know Y whose value is 3, Y thinks X can have 2 values 2 or 4 (Y-1 or Y+1) Since X says that now he/she got the value of Y Y can rule out X=4. If X was 4 it cannot understand value of Y.

So X=2 and Y=3

Let us consider two combinations: 2,3 and 3,4. Why? Because the only case when Yvette knows Xanthe's number (or vice versa) right away is when her number is 1. Therefore, neither Xanthe's nor Yvette's number is 1. If Xanthe's number is 2, the only numbers that are consecutive in pair with 2 are 1 and 3. Because Yvette's number is not 1, the only remaining option is 3. Then consider a scenario in which Xanthe's number is 3, which implies that Yvette's number is either 2 or 4. If her number is 2, she already knows Xanthe's number is 3, since it's not 1. Because she doesn't know Xanthe's number, her number must in fact be 4.

Looks harder than it is!

It can't be 1 or 5, because then it can't be consecutive. The remaining options are 2,3,4. If they're consecutive pairs, it has to be 2-3, or 3-4 - meaning 3 is for sure one of the numbers!

First Xanthe said I dont know your number. This remove 1 and 5 from the selection because if Xanthe got 1 she defenitely knew that Yvette got 2 and if she got 5 she knew Yvette got 4. Second Yvette said I dont know you number, meaning she also doesnt have the number 1 and 5. This gives two possible cases - they got 2 and 3 -or they got 3 and 4 In both cases number 3 must be one of Zebedee's numbers. more.... Yvette doesn t really know Xanthe s number because she have the number 3.

First, let's look at the list of positive, consecutive numbers: 1,2,3,4,5,6,7,...

Now, the root idea of this problem is:

"The person who gets 1, will know the other number, as its only positive neighbouring number is 2 (0 isn't positive)".

More general, a person will know the other number when they can exclude one of the two options.

Let's look at the possible numbers per person:

When X says she doesn't know her number, she can't have 1.

When Y says she doesn't know her number, she can't have 1 or 2 (as she knows X does not have 1).

The resulting possible numbers per person:

When now X says she knows her number, she can have 2 or 3. As Y cannot have 1 or 2.

When now Y says she knows her number, she can have 3 or 4. As X can only have 2 or 3.

The only possible pairs are (2,3) and (3,4). Thus the number 3 must be one of Zebedee's numbers.

Neither woman has 1 or 5 because if they did, they would know the other person's number was 2 or 4 respectively. That means that the two numbers come from the set of 2, 3 and 4. Three has to be one of the numbers - since the numbers are consecutive, the choice of 2 and 4 is eliminated. The choices are 2 and 3 or 3 and 4.

This solution was submitted by my friend Paul Kalmar, so if you happen to select this answer, give him the book... he's a friggin' genius , Thank you...

" It's a strange multiple choice question, as there are exactly two numbers possible and both are listed as choices. 2 and 3. The only number which would tell the other the answer is 1. Saying that they don't know the other number means they do not have 1. This is only informative if the number they have is 2, as the only remaining choice for other number is 3. Knowing that this solved the problem, the one with 3 knows the other has 2. "

-Paul Kalmar

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Now here's my logic:

If either girl had the number 1, they would know that other girl had the number 2

But since neither girl had the number 1, Yvette and Xanethe now have all of the information that they need:

Yvette now knows for sure that Xanethe's number must be 3, seeing that neither of them have 1 and that would be only other consecutive number to the number 2, however, if she declares that she "knows" Xanethe's number, that still would leave Xanethe with two choices for Yvette (2 or 4) , so Xanethe still needs more information:

By telling Yvette "Now I know you're number " gives Yvette the chance to either:

A) Declare that she knows Xanethe's number. Which means that Yvette does not have two numbers to guess from...she only has one number to guess from. And since the number 1 has been ruled out, number 2 is the only number left that now has one consecutive number to choose from (number 3.), Yvette must have the number 2.

....OR.....

B) Yvette will declare that she still does not know Xanethe's number, which means that she has two possible numbers to guess from (3 or 5), meaning that Yvette would have the number 4.

Xanethe delcaring that she now "knows" Yvette's number, gives Yvette the chance to confirm to Xanethe, if Yvette has the number 2 or the number 4

However, in either scenario, Xanethe's number must be 3...

One of the Zebedee's +ve integer is 3

Solution :

If Xanthe had 1, Yvette would have 2

But Xanthe would already know the two consecutive +ve integers

If Yvette had 1, Xanthe would have 2

But Yvette would already know the two consecutive +ve integers

Therefore 1 is not the possible integer

If Xanthe had 5, Yvette - 4 (6 isn't an option)

But Xanthe would already know the two consecutive +ve integers

If Yvette -5, Xanthe - 4

Yvette would already know the two consecutive +ve integers

Therefore 5 isn't a possible integer

Thus options left are numbers 2, 3, 4

If Xanthe had 2 then Yvette - 3

& if Yvette had 2, Xanthe - 3

If Xanthe had 3, Yvette - 4

& If Yvette - 3 then Xanthe - 4

Both conditions are having 3 in common,

thus we can assume that one of the Zebedee's +ve integer is 3

//saw this question on Facebook, and posted the answer there, then joined brilliant, it's brilliant, reposting it here//

Yes, it's 3, but you cannot use the 5 logic because the problem only states that the girls are given positive consecutive numbers. They are not told that the numbers must be less than or equal to 5. We know that for our multiple choice options, but that information was not given to the girls and it was not needed.

Neither girl can have a 1 or a 5 since, in that case, they would know the other had a 2 or a 4. Of the remaining three numbers the only consecutive pairs are 2,3 or 3,4 each of which contain a 3. QED

The first person saying "I don't know yours", tells the second one that the first person cannot have 1 or 5, so must be 2, 3, 4. The second person replying that "I don't know yours" means that the second person cannot have 2 or 4, nor 1 or 5, so she must have 3.

If one of the number is '1' then other girl would have surely said that she know what is second number because only possible option will be `2'. Similar case for '5'. So only possible option remains "2 and 3" or "3 and 4". Therefore 3 is one of the number.

The key to solving this problem is the fact that the two numbers are consecutive.

Let's start by using Xanthe's first statement that she doesn't know Yvette's number:

• If Xanthe had a 1, she would know that Yvette has a 2 because their numbers are consecutive, and she would have said "I know your number!"
• If Xanthe had a 5, she would also know that Yvette has a 4, again because their numbers are consecutive.

However, because Xanthe doesn't know Yvette's number, we can eliminate these possibilities. Xanthe's number is either 2, 3, or 4.

Yvette knows all of this because Xanthe said she doesn't know Yvette's number. But before declaring that she doesn't know Xanthe's number either, she takes note of the following:

• If Yvette had a 1, she would know that Xanthe has a 2 because their numbers are consecutive.
• If Yvette had a 5, she would know that Xanthe has a 4.
• If Yvette had a 2, she would know that Xanthe has a 3. This is because Xanthe doesn't have a 1, as explained above.
• If Yvette had a 4, she would also know that Xanthe has a 3, because Xanthe doesn't have a 5.

These statements eliminate all possibilities for Yvette except for 3, and now Xanthe knows that Yvette has a 3. This is the answer to the problem.

There is a fourth statement: Yvette also knows Xanthe's number! However, this is not true. There are two possibilities for Xanthe's number (2 and 4), and no more information can be obtained. Yvette is just guessing :)