## A Lewis Carroll logic problem.

Problem: To achieve the complete conclusion.

1. When the day is fine, I tell Froggy "You're quite the dandy, old chap!";
2. Whenever I let Froggy forget that 10 pounds he owes me, and he begins to strut about like a peacock, his mother declares "He shall not go out a-wooing!";
3. Now that Froggy's hair is out of curl, he has put away his gorgeous waistcoat;
4. Whenever I go out on the roof to enjoy a quiet cigar, I'm sure to discover that my purse is empty;
5. When my tailor calls with his little bill, and I remind Froggy of that 10 pounds he owes me, he does not grin like a hyena;
6. When it is very hot, the thermometer is high;
7. When the day is fine, and I'm not in the humor for a cigar, and Froggy is grinning like a hyena, I never venture to hint that he's quite the dandy;
8. When my tailor calls with his little bill and finds me with an empty pocket, I remind Froggy of that 10 pounds he owes me;
9. My railway shares are going up like anything!
10. When my purse is empty, and when, noticing that Froggy has got his gorgeous waistcoat on, I venture to remind him of that 10 pounds he owes me, things are apt to get rather warm;
11. Now that it looks like rain, and Froggy is grinning like a hyena, I can do without my cigar;
12. When the thermometer is high, you need not trouble yourself to take an umbrella;
13. When Froggy has his gorgeous waistcoat on, but is not strutting about like a peacock, I betake myself to a quiet cigar;
14. When I tell Froggy that he's quite a dandy, he grins like a hyena;
15. When my purse is tolerably full, and Froggy's hair is one mass of curls, and when he is not strutting about like a peacock, I go out on the roof;
16. When my railways shares are going up, and when it's chilly and looks like rain, I have a quiet cigar;
17. When Froggy's mother lets him go a-wooing, he seems nearly mad with joy, and puts on a waistcoat that is gorgeous beyond words;
18. When it is going to rain, and I am having a quiet cigar, and Froggy is not intending to go a-wooing, you had better take an umbrella;
19. When my railway shares are going up, and Froggy seems nearly mad with joy, that is the time my tailor always chooses for calling with his little bill;
20. When the day is cool and the thermometer low, and I say nothing to Froggy about his being quite the dandy, and there's not the ghost of a grin on his face, I haven't the heart for my cigar!

### Dictionary for Froggy's Problem

a = Froggy's hair is out of curl
b = Froggy intends to go a-wooing
c = Froggy is grinning like a hyena
d = Froggy's mother permits him to go a-wooing
e = Froggy seems nearly mad with joy
h = Froggy is strutting about like a peacock
k = Froggy is wearing a waistcoat that is gorgeous beyond words
l = I go out on my roof
m = I remind Froggy of the 10 pounds he owes me
n = I take a quiet cigar
r = I tell Froggy that he's quite the dandy
s = It is going to rain
t = It is very hot
v = My purse is empty
w = My railway shares are going up
z = My tailor calls with his little bill
A = The thermometer is high
B = You had better take an umbrella

### Conjectures about the language of the puzzle

• "The day is fine" is the opposite of "it is going to rain."
• "I'm not in the humor for a cigar" is the opposite of "I take a quiet cigar."
• "Things are apt to get rather warm" is not a figure of speech meaning that Froggy's going to get angry at me, but rather means "it is very hot."
• "I can do without my cigar" is the same as "I don't take a quiet cigar."
• "It looks like rain" also means "the day is not fine."
• "There's not the ghost of a grin on his (Froggy's) face" implies that he is NOT feeling nearly mad with joy.
• Statement 9 is meant to be a statement of fact -- that clause "w" is true.
• Statement 3 is meant to be a statement that claus "a" is true and clause "k" is false.

• Statement 11 says that "s", "c", and "n" are all true.