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.)

I got 357 just like the others, but in case anyone out there was lost about how to approach the problem, here's what I did. (Of course there are many other approaches)

First, look at Questions (3) and (5). Let's say the answer to Question (5) was that the number is divisible by 15. If that is the case, then we have a problem with Question (3) because then both 3 and 5 would be true. Since there can only be exactly one right answer, clearly the answer to Question (5) cannot be 15.

Going back to Question (5), if we find all the numbers divisible by 17, and all the numbers divisible by 19, we get 103 numbers. Plus, 3 of those are divisible by both 17 and 19, so we actually get down to 100 numbers.

Next, by looking at Question (6) we can knock off the first digit of the number and see if they are divisible by 19 or 20. Once we do that, we are left with nine numbers: 119, 238, 340, 357, 380, 476, 595, 680, and 760.

Considering Question (4), only three of these numbers are either strictly increasing (238, 357) or strictly decreasing (760).

And finally, looking at Question (8) for these three numbers, we get that the differences are 6, 4, and 7. Since we aren't given 6 and 7 as choices, the answer must the one that corresponds to the difference of 4... 357.

Posted by nikki on 2003-08-28 19:18:14