Reading emails scrambled by Eudora

Eudora is the best email program there is, but it is dead. Being dead, it cannot be upgraded to display messages with international characters in them. “Saumon fumé” is displayed as “Saumon fumé”, but “Wędzony łosoś” is displayed as “WÄ™dzony Å‚osoÅ›”.

If you get such a scrambled email, here are two ways of reading it.

On the web

Visit this converter page and copy and paste the received email into it.

On your computer (Windows)

  1. Open Notepad. (If you can’t see an icon for it, hold down the Windows key, press R, and then type notepad into the box).
  2. Paste the received email into it.
  3. Go back to the beginning of the email, and post the following three characters into it, with no spaces between them: ï»¿
  4. Save the document. In the “Encoding” box in the Save window, make sure “ANSI” is selected.
  5. Close Notepad.
  6. Open the saved document. It will now be readable.

 

 

A ridiculous puzzle: the end

To recapitulate: I think of two numbers greater than 1. I add them together and give them to Anna. I multiply them together and give them to Mark. Anna and Mark are perfect logicians and perfectly truthful. They have a conversation together about whether they know the numbers I thought of or not.

In Round 1, Mark spoke. He said whether or not he knew what numbers I had thought of (or, equivalently, what Anna’s total was). In Round 2, Anna spoke. In Round 3, Mark spoke. In Round 4, Anna spoke. In Round 5, Marl spoke. In Round 6, Anna spoke. Here is the chart showing what my numbers could be and what Mark’s and Anna’s answer would be in each case. M means that Mark says ‘I know’, A means that Anna says ‘I know’. A dot indicates a ‘don’t know’.

2 3 4 5 6 7 8 9 10 11
2 MA MA M.. MA ..MA MA ….MA ….. ….. MA
3 MA M. .AM MA ….. M. ….. M. ….. M.
4 M. .AM …AM ….. …..A ….. ….. ….. ….. …..
5 MA MA ….. M. ….. M. ….. ….. ….. M.
6 ..MA ….. …..A ….. ….. ….. ….. ….. ….. …..
7 MA M. ….. M. ….. M. ….. ….. ….. M.
8 ….MA ….. ….. ….. ….. ….. ….. ….. ….. …..
9 ….. M. ….. ….. ….. ….. ….. ….. ….. …..
10 ….. ….. ….. ….. ….. ….. ….. ….. ….. …..
11 MA M. ….. M. ….. M. ….. ….. ….. M.

Now it is Mark’s turn again.

Considering the numbers Mark doesn’t yet know the answer to, the only interesting case is if Mark sees 24. 24 can be 2×12 or 3×8 or 4×6.

  1. If the numbers are 2 and 12 then Anna will never have said ‘I know’. (This is not visible in the table, which would have to be drawn bigger to show it).
  2. If the numbers are 3 and 8 then Anna will never have said ‘I know’.
  3. If the numbers are 4 and 6 then Anna will just have said ‘I know’.

If Anna has just said ‘I know’, then Mark can deduce that the numbers are 4 and 6. But if Anna has just said ‘I don’t know’, then Mark can deduce nothing at all, because the numbers could be 2 and 12 or 3 and 8.

Mark can deduce nothing new from Anna’s saying ‘I don’t know’, so the game is at an end.

A ridiculous puzzle: Round 6

To recapitulate: I think of two numbers greater than 1. I add them together and give them to Anna. I multiply them together and give them to Mark. Anna and Mark are perfect logicians and perfectly truthful. They have a conversation together about whether they know the numbers I thought of or not.

In Round 1, Mark spoke. He said whether or not he knew what numbers I had thought of (or, equivalently, what Anna’s total was). In Round 2, Anna spoke. In Round 3, Mark spoke. In Round 4, Anna spoke. In Round 5, Marl spoke. Here is the chart showing what my numbers could be and what Mark’s and Anna’s answer would be in each case. M means that Mark says ‘I know’, A means that Anna says ‘I know’. A dot indicates a ‘don’t know’.

2 3 4 5 6 7 8 9 10 11
2 MA MA M.. MA ..MA MA ….M ….. ….. MA
3 MA M. .AM MA ….. M. ….. M. ….. M.
4 M. .AM …AM ….. ….. ….. ….. ….. ….. …..
5 MA MA ….. M. ….. M. ….. ….. ….. M.
6 ..MA ….. ….. ….. ….. ….. ….. ….. ….. …..
7 MA M. ….. M. ….. M. ….. ….. ….. M.
8 ….M ….. ….. ….. ….. ….. ….. ….. ….. …..
9 ….. M. ….. ….. ….. ….. ….. ….. ….. …..
10 ….. ….. ….. ….. ….. ….. ….. ….. ….. …..
11 MA M. ….. M. ….. M. ….. ….. ….. M.

Now it is Anna’s turn again.

Considering the numbers Anna doesn’t yet know the answer to, the only interesting case is if Anna sees 10. 10 can be 2+8 or 3+7 or 4+6 or 5+5.

  1. If the numbers are 2 and 8 then Mark will just have said ‘I know’.
  2. If the numbers are 3 and 7 then Mark will have said ‘I know’ a long time ago.
  3. If the numbers are 4 and 6 then Mark will never have said ‘I know’.
  4. If the numbers are 5 and 5 then Mark will have said ‘I know’ a long time ago.

In both cases 1 and 3, Anna can now deduce the answer (in cases 2 and 4, she still can’t). Here is the new chart:

2 3 4 5 6 7 8 9 10 11
2 MA MA M.. MA ..MA MA ….MA ….. ….. MA
3 MA M. .AM MA ….. M. ….. M. ….. M.
4 M. .AM …AM ….. …..A ….. ….. ….. ….. …..
5 MA MA ….. M. ….. M. ….. ….. ….. M.
6 ..MA ….. …..A ….. ….. ….. ….. ….. ….. …..
7 MA M. ….. M. ….. M. ….. ….. ….. M.
8 ….MA ….. ….. ….. ….. ….. ….. ….. ….. …..
9 ….. M. ….. ….. ….. ….. ….. ….. ….. …..
10 ….. ….. ….. ….. ….. ….. ….. ….. ….. …..
11 MA M. ….. M. ….. M. ….. ….. ….. M.

So we have the fifth interesting answer in the game.

Mark: Don’t know; Anna: I don’t know; Mark: I don’t know; Anna: I don’t know; Mark: I don’t know; Anna: I know – can only mean that the numbers are 4 and 6. Mark’s number is 24 and Anna’s number is 10.

Next, it is Mark’s turn. Now that he has heard what Ann has said, we shall see what he can deduce.

A ridiculous puzzle: Round 5

To recapitulate: I think of two numbers greater than 1. I add them together and give them to Anna. I multiply them together and give them to Mark. Anna and Mark are perfect logicians and perfectly truthful. They have a conversation together about whether they know the numbers I thought of or not.

In Round 1, Mark spoke. He said whether or not he knew what numbers I had thought of (or, equivalently, what Anna’s total was). In Round 2, Anna spoke. In Round 3, Mark spoke. In Round 4, Anna spoke. Here is the chart showing what my numbers could be and what Mark’s and Anna’s answer would be in each case. M means that Mark says ‘I know’, A means that Anna says ‘I know’. A dot indicates a ‘don’t know’.

2 3 4 5 6 7 8 9 10 11
2 MA MA M.. MA ..MA MA …. …. …. MA
3 MA M. .AM MA …. M. …. M. …. M.
4 M. .AM …A …. …. …. …. …. …. ….
5 MA MA …. M. …. M. …. …. …. M.
6 ..MA …. …. …. …. …. …. …. …. ….
7 MA M. …. M. …. M. …. …. …. M.
8 …. …. …. …. …. …. …. …. …. ….
9 …. M. …. …. …. …. …. …. …. ….
10 …. …. …. …. …. …. …. …. …. ….
11 MA M. …. M. …. M. …. …. …. M.

Now it is Mark’s turn again.

Considering the numbers Mark doesn’t yet know the answer to, the only interesting case is if Mark sees 16. 16 can be 2×8 or 4×4.

  1. If the numbers are 2 and 8 then Anna will never have said ‘I know’.
  2. If the numbers are 4 and 4 then Anna will just have said ‘I know’.

So in both cases 1 and 2, Mark can now deduce the answer. Here is the new chart:

2 3 4 5 6 7 8 9 10 11
2 MA MA M.. MA ..MA MA ….M ….. ….. MA
3 MA M. .AM MA ….. M. ….. M. ….. M.
4 M. .AM …AM ….. ….. ….. ….. ….. ….. …..
5 MA MA ….. M. ….. M. ….. ….. ….. M.
6 ..MA ….. ….. ….. ….. ….. ….. ….. ….. …..
7 MA M. ….. M. ….. M. ….. ….. ….. M.
8 ….M ….. ….. ….. ….. ….. ….. ….. ….. …..
9 ….. M. ….. ….. ….. ….. ….. ….. ….. …..
10 ….. ….. ….. ….. ….. ….. ….. ….. ….. …..
11 MA M. ….. M. ….. M. ….. ….. ….. M.

So we have the fourth interesting answer in the game.

Mark: Don’t know; Anna: I don’t know; Mark: I don’t know; Anna: I don’t know; Mark: I know – can only mean that the numbers are 2 and 8. Mark’s number is 16 and Anna’s number is 10.

Next, it is Anna’s turn. Now that she has heard what Mark has said, we shall see what she can deduce.

A ridiculous puzzle: Round 4

To recapitulate: I think of two numbers greater than 1. I add them together and give them to Anna. I multiply them together and give them to Mark. Anna and Mark are perfect logicians and perfectly truthful. They have a conversation together about whether they know the numbers I thought of or not.

In Round 1, Mark spoke. He said whether or not he knew what numbers I had thought of (or, equivalently, what Anna’s total was). In Round 2, Anna spoke. In Round 3, Mark spoke. Here is the chart showing what my numbers could be and what Mark’s and Anna’s answer would be in each case. M means that Mark says ‘I know’, A means that Anna says ‘I know’. A dot indicates a ‘don’t know’.

2 3 4 5 6 7 8 9 10 11
2 MA MA M.. MA ..M MA MA
3 MA M. .AM MA M. M. M.
4 M. .AM
5 MA MA M. M. M.
6 ..M
7 MA M. M. .. M. .. .. .. M.
8
9 M.
10
11 MA M. M. M. M.

Now it is Anna’s turn again. Anna knows more than she did last time, because she knows whether or not Mark had managed to deduce the numbers, taking into account what he saw in front of him and what she had said before.

Considering the numbers Anna doesn’t yet know the answer to, the only interesting case is if Anna sees 8. 8 can be 2+6 or 3+5 or 4+4.

  1. If the numbers are 2 and 6 then Mark will just have said ‘I know’.
  2. If the numbers are 3 and 5 then Mark will have said ‘I know’ a long time ago (and Anna will have said ‘I know’ as well).
  3. If the numbers are 4 and 4 then Mark will not have said ‘I know’ at all.

So in both cases 1 and 3, Anna will now have deduced the answer (and in case 2 she has known it for some time). Here is the new chart:

2 3 4 5 6 7 8 9 10 11
2 MA MA M.. MA ..MA MA …. …. …. MA
3 MA M. .AM MA …. M …. M. …. M.
4 M. .AM …A …. …. …. …. …. …. ….
5 MA MA …. M. …. M. …. …. …. M.
6 ..MA …. …. …. …. …. …. …. …. ….
7 MA M …. M. …. M. …. …. …. M.
8 …. …. …. …. …. …. …. …. …. ….
9 …. M. …. …. …. …. …. …. …. ….
10 …. …. …. …. …. …. …. …. …. ….
11 MA M. …. M. …. M. …. …. …. M.

So we have the third interesting answer in the game.

Mark: Don’t know; Anna: I don’t know; Mark: I don’t know; Anna: I know – can only mean that the numbers are 4 and 4. Mark’s number is 16 and Anna’s number is 8.

Next, it is Mark’s turn. Now that he has heard what Anna has said, we shall see what he can deduce.

A ridiculous puzzle: Round 3

To recapitulate: I think of two numbers greater than 1. I add them together and give them to Anna. I multiply them together and give them to Mark. Anna and Mark are perfect logicians and perfectly truthful. They have a conversation together about whether they know the numbers I thought of or not.

In Round 1, Mark spoke. He said whether or not he knew what numbers I had thought of (or, equivalently, what Anna’s total was). In Round 2, Anna spoke. Here is the chart showing what my numbers could be and what Mark’s and Anna’s answer would be in each case. M means that Mark says ‘I know’, A means that Anna says ‘I know’. A dot indicates a ‘don’t know’.

2 3 4 5 6 7 8 9 10 11
2 MA MA M. MA .. MA .. .. .. MA
3 MA M. .A MA .. M .. M .. M.
4 M. .A .. .. .. .. .. .. .. ..
5 MA MA .. M. .. M. .. .. .. M.
6 .. .. .. .. .. .. .. .. .. ..
7 MA M .. M. .. M. .. .. .. M.
8 .. .. .. .. .. .. .. .. .. ..
9 .. M. .. .. .. .. .. .. .. ..
10 .. .. .. .. .. .. .. .. .. ..
11 MA M. .. M. .. M. .. .. .. M.

Now it is Mark’s turn again. Mark knows more than he did last time, because he knows whether or not Anna had managed to deduce the numbers, taking into account what she saw in front of her and what Mark said before.

Considering the numbers Mark doesn’t yet know the answer to, the only interesting case is if Mark sees 12. 12 can be 2×6 or 3×4. If the numbers are 3 and 4 then Anna has just said ‘I know’ in Round 2. If the numbers are 2 and 6 then Anna has just said ‘I don’t know’ in Round 2. In both cases, Mark can now deduce what the numbers are, and say ‘I know’.

So here is the new chart:

 

2 3 4 5 6 7 8 9 10 11
2 MA MA M.. MA ..M MA MA
3 MA M. .AM MA M M. M.
4 M. .AM
5 MA MA M. M. M.
6 ..M
7 MA M M. .. M. .. .. .. M.
8
9 M.
10
11 MA M. M. M. M.

So we have the second interesting answer in the game.

Mark: Don’t know; Anna: I don’t know; Mark: I know – can only mean that the numbers are 2 and 6. Mark’s number is 12 and Anna’s number is 8.

Next, it is Anna’s turn. Now that she has heard what Mark has said, we shall see what she can deduce.

A ridiculous puzzle: Round 2

To recapitulate: I think of two numbers greater than 1. I add them together and give them to Anna. I multiply them together and give them to Mark. Anna and Mark are perfect logicians and perfectly truthful. They have a conversation together about whether they know the numbers I thought of or not.

In Round 1, Mark spoke. He said whether or not he knew what numbers I had thought of (or, equivalently, what Anna’s total was). Here is the chart showing what my numbers could be and what Mark’s answer would be in each case:

2 3 4 5 6 7 8 9 10 11
2 M M M M . M . . . M
3 M M . M . M . M . M
4 M . . . . . . . . .
5 M M . M . M . . . M
6 . . . . . . . . . .
7 M M . M . M . . . M
8 . . . . . . . . . .
9 . M . . . . . . . .
10 . . . . . . . . . .
11 M M . M . M . . . M

Now it is Anna’s turn. Anna sees her number, which is the sum of the numbers I thought of, and she has also heard Mark’s statement – ‘I know what the numbers are’ or ‘I don’t know what the numbers are’. Here are some possibilities:

  1. Anna sees 7, and hears Mark saying ‘I know’. 7 could be 2+5 or 3+4. From the chart, if the numbers were 2 and 5, Mark would have said ‘I know’ and if they were 3 and 4 Mark would have said ‘I don’t know’. So now Anna knows that the numbers must be 2 and 5.
  2. Anna sees 7, and hears Mark saying ‘I don’t know’. 7 could be 2+5 or 3+4. From the chart, if the numbers were 2 and 5, Mark would have said ‘I know’ and if they were 3 and 4 Mark would have said ‘I don’t know’. So now Anna knows that the numbers must be 3 and 4.
  3. Anna sees 8, and hears Mark saying ‘I know’. 8 could be 2+6 or or 3+5 or 4+4. From the chart, if the numbers were 3 and 5, Mark would have said ‘I know’ and if they were 2 and 6 or 4 and 4 then Mark would have said ‘I don’t know’. So now Anna knows that the numbers must be 3 and 5.
  4. Anna sees 8, and hears Mark saying ‘I don’t know’. 8 could be 2+6 or or 3+5 or 4+4. From the chart, if the numbers were 3 and 5, Mark would have said ‘I know’ and if they were 2 and 6 or 4 and 4 then Mark would have said ‘I don’t know’. So now Anna knows that the numbers must be 2 and 6 or 4 and 4, but she doesn’t know which. Anna doesn’t know the numbers, and never will.

Applying this reasoning throughout, here is the chart after round 2. The first character is M if Mark said ‘I know’ and a dot if he didn’t. The second character is A if Anna said ‘I know’ and a dot if she didn’t.

2 3 4 5 6 7 8 9 10 11
2 MA MA M. MA .. MA .. .. .. MA
3 MA M. .A MA .. M .. M .. M.
4 M. .A .. .. .. .. .. .. .. ..
5 MA MA .. M. .. M. .. .. .. M.
6 .. .. .. .. .. .. .. .. .. ..
7 MA M .. M. .. M. .. .. .. M.
8 .. .. .. .. .. .. .. .. .. ..
9 .. M. .. .. .. .. .. .. .. ..
10 .. .. .. .. .. .. .. .. .. ..
11 MA M. .. M. .. M. .. .. .. M.

So we have the first interesting answer in the game.

Mark: Don’t know; Anna: I know – can only mean that the numbers are 3 and 4. Mark’s number is 12 and Anna’s number is 7.

Next, it is Mark’s turn. Now that he has heard what Anna has said, we shall see what he can deduce.

A ridiculous puzzle: Round 1

To recapitulate: I think of two numbers greater than 1. I add them together and give them to Anna. I multiply them together and give them to Mark. Anna and Mark are perfect logicians and perfectly truthful. They have a conversation together about whether they know the numbers I thought of or not.

In Round 1, it is Mark’s turn to speak. Here is a chart of what he will say, depending on the two numbers I thought of:

2 3 4 5 6 7 8 9 10 11
2 M M M M . M . . . M
3 M M . M . M . M . M
4 M . . . . . . . . .
5 M M . M . M . . . M
6 . . . . . . . . . .
7 M M . M . M . . . M
8 . . . . . . . . . .
9 . M . . . . . . . .
10 . . . . . . . . . .
11 M M . M . M . . . M

M indicates that Mark has been able to deduce the two numbers; a dot means that he hasn’t.

Mark can deduce the two numbers in the following circumstances:

  1. Both the numbers are primes. For instance, if Mark is given 3×5=15, 15 can only be written as 3×5 or 5×3, so Mark will know that the numbers are 3 and 5. I have marked these cases in black in the table.
  2. One number is a prime and the other number is its square. For instance, if Mark is given 2×4=8, 8 can only be written as 2×4 or 4×2, so Mark will know that the numbers are 2 and 4. The same thing does not apply to cubes. If Mark is given 2×8=16, that can be 2×8 or 4×4, and Mark can’t tell which is is. I have marked these cases in red in the table.

In every other case, Mark can’t tell what the numbers are. For instance, if he is given 3×4=12, he will see 12 but he will not be able to decide whether that comes from 3×4 or 2×6.

Next, it is Anna’s turn, and we shall see what she can deduce.

Some Urgent Reforms: The Human Circulating Library

In the following reflections, my only intention is to suggest a few plain and practical reforms in our modern life — Utopian and revolutionary fancies I leave to the visionary and the poet, and the first of the institutions, for which I feel that society is crying out, is the “Human Circulating Library.” In other words, it is crying out for a Mr. Mudie, who, instead of circulating books, should circulate people.

It is generally supposed that we all believe the soul to be more important than the body, the internal condition more valid than the external act. And yet it is singular to reflect that if this conception were actually carried out in our civilisation, that civilisation would seem a city built by madmen, a prodigy to the sun and stars. In such a city it would not be important actions or sensational accidents that would be reported in the newspapers, but important emotions and sensational frames of mind. Special editions of the evening papers would declare in sprawling head lines not the fact that Botha had captured two hundred Canadians and the war was over; they would announce that Mr. Robinson, of Leeds, was in a state of spiritual exhilaration, or that seventeen persons in Paddington Green had been stricken with a rich and pensive sadness.

Such strange and pleasing sights we should see if men actually realised how much more important is the inward than the outward life, and the heart than the head. In no case would the principle be more revolutionary than in the case I have already mentioned, the case of circulating libraries. In this materialistic civilisation of ours, we insist that Mr. Mudie shall be compensated if a man has damaged his book. But who speaks of any compensation when a book has damaged a man? Who attempts to punish the slovenly and unscrupulous volume which has dog-eared a man’s opinions, soiled his ideal, torn out the coloured pictures of memory and pride? How startled Mr. Mudie would be if he received an account claiming so much for destruction of beliefs, so much for unnecessary horror, so much for waste of time. In this matter again, there would be a whole Stock Exchange of practical commerce if we realised that the soul is more than the body.

But the institution of circulating libraries is capable, as I have hinted, of another and much wider and more inspiring development. The great curse of our civilisation is that it is so large that whole masses of its inhabitants never see any but one side of life, any but one phase of thought. The modern world is so broad that all its citizens are narrow. There were a great many advantages in living in a small State, one of them was that of living in a larger world. In Athens probably a man could not put his nose outside his door without hearing Mystics and Atheists talking at the top of their voices. To-day there are whole tracts of country such as Brixton and Surbiton in which the householder might go out in perfect safety, in which great philosophers do not argue in the street, perhaps from one year’s end to another. These vast herds of suburban citizens living perpetually among people like themselves, might, indeed, be rescued to some extent from ignorance of others and of current thought by the daily Press. But here again the party system frustrates us, and a man only reads in his daily paper his own prejudices embellished with other people’s arguments. Something must be done to shift and float these vast clogged and stagnant masses of human life. Unless this is done it will be no idle jest to say that our civilisation is melting away in an apocalypse which it has not even the sense to understand. We require, in short, first and foremost, a quicker circulation of the civic blood.

The “Human Circulating Library” might be conducted either as an individual or a State concern. It would be arranged on a simple principle. All those who were members of it would hold themselves ready during certain specified months of the year to stay at the houses of any other members who had taken them out of the library. In return, of course, they would themselves have the privilege of taking other people out of the library. The subscriber would send a postcard to the librarian saying, “Send me Mr. Smiles, Professor Puffy, and Unterbringen, the German Anarchist.” The librarian would reply that Professor Puffy was out at present, and that by the new regulations of circulating libraries it was impossible to procure more than one copy of the same man. He would also beg to remind the subscriber that he had already kept Miss MacDermott beyond the proscribed time, and that a penny per day was charged for the delay. At the end of the week not Mudie’s cart, but Mudie’s comfortable private omnibus would arrive and deposit two Dissenting preachers and an African explorer, with all their luggage, at the gate. Any person damaging a man would be required to make him good.

To those duller sceptics who have in every age discouraged great and practical reforms, this scheme may seem to verge even upon the fantastic. Some elements certainly there are in it which might lead to a seemingly extravagant development. Local officials might announce that owing to the kindness of Lady Warmer, “Major Barker” had been added to the library, and philanthropists might gain a reputation for munificence by giving whole sets of maiden ladies to so deserving an institution. But however unfamiliar at first the customs and phraseology of the “Human Circulating Library” might appear, its essential results would be full of unfathomable wisdom and profit. Men would begin to realise that a man is not only the most deep and vital, but the most entertaining of all studies. Ambitious young students would talk about being at work on “Wilkins” and getting up “Montmorenci.” There would in many places be two professors, nay, two schools of thought, with different theories of the same old gentleman. Some ardent young sociologist would begin with great pride with being engaged on “Miss Butterworth,” and end by being engaged to her.

I have dealt only with a few examples of the practical and even prosaic side of the scheme. Of its moral and spiritual utility and urgency I can hardly speak sufficiently. It would break down that barrier the last, the silliest and the most insolent of class barriers, more narrow and unmeaning than that between freemen and slaves, the barrier between the people we do know and the people we do not. It would erase that monstrous irony which will suddenly strike the traveller who finds himself at night alone in a long street walled on both sides by the hives of his brothers. It would destroy that last and darkest of Cosmic jests, whereby a desert can be made of houses. It will wake us all suddenly to the thought that we are all living on a desert island and have never spoken to each other.

 G.K. Chesterton

 

A ridiculous puzzle

I think of two numbers greater than 1 (they may or may not be the same number).

I add these two numbers together and give them to my friend Anna. I multiply the same two numbers together and give them to my friend Mark. Both my friends are perfectly truthful and perfect logicians.

  1. M says to A: ‘I don’t know what your number is’.
  2. A says to M: ‘I don’t know what your number is’.
  3. M says to A: ‘I don’t know what your number is’.
  4. A says to M: ‘I don’t know what your number is’.
  5. M says to A: ‘I don’t know what your number is’.
  6. A says to M: ‘I know what your number is’.
  7. M says to A: ‘I know what your number is’.

Question. What are Anna’s and Mark’s numbers? (Or, equivalently: what numbers did I originally think of?)

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