The teacher explains, "Now take out your homework class, and answer these questions about the number you calculated for homework. Remember, it was a positive integer no more than 1000."

1 Is the number
A) Less than 100
B) Less than 900
C) Greater than 900

2 Is the sum of the digits
A) Greater than 10
B) Greater than 20
C) Greater than 30

3 Is the number divisible by:
A) 2
B) 3
C) 5

4 Are the digits:
A) Strictly increasing
B) Strictly decreasing

5 Is the number divisible by:
A) 15
B) 17
C) 19

6 If you get rid of the number's first digit, is it divisible by:
A) 19
B) 20

7 When spelled out, does the spelling use:
A) J
B) L
C) Q
D) V
E) X
F) Z

8 Ignoring the sign, what is the difference between the hundred's digit and the one's digit?
A) 2
B) 3
C) 4
D) 5

9) How many times does the letter E appear when the word is spelled out?
A) 3
B) 5
C) 7

10 Is the first digit of the number
A) Odd
B) Even

You panic, because you were too busy last night solving other things on flooble and didn't get a chance to do your homework. But when you figure out the quiz (where exactly one answer is right per question), you see that only one number will work.

What is this number?

(Note: Spelled out means in words. For example: 123 is "One hundred twenty three". Divisible means divided with no remainder. Also, padding the number with leading zeroes isn't allowed.)

(In reply to re: Minimal Brute Force by Talon5000)

"Brute force" would be like going through all the numbers from 1 to 1000 and eliminating them one at a time.
Other people listed out all the multiples of 19 and 20, and went through each of those numbers (a form of brute force or trial-and-error), which is obviously better, but not ideal.

The only brute force in my solution was listing out the 5 two-digit multiples of 19, and going through the final three choices for the number. Everything else was based on logical deductions, directly from the clues, to minimize the trial-and-error that would need to be done.

A computer program is a form of brute force (as Charlie has humorously noted) since it really goes through all possible numbers until it finds a match (although it goes much faster than we could ever go through them).

Posted by DJ on 2003-08-29 22:57:43