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.)

Since teacher says the number is not greater than a thousand is must either be 1000 or be less. Q2 indicates that the sum of the digits must be greater than 10 (at least) so the answer can't be 1000 therefore the maximum number of possible digits in the number is 3.

Q6 indicates that if you remove teh first digit the remaining digits are divisible by one of two two digits numbers (19 and 20) all numbers divisible by 2 digit numbers must have at least two digits therefore the minimum number of digits in our response must be three
THEREFORE we are looking for a three digit number.

Q6 also indicates that the last two digits must be divisible by 19 or 20. They, however, can not be divisible by 20 because any number ending in a figure divisible by 20 would also be divisible by 20 and therefore divisible by both 2 and 5 but Q3 can only have 1 answer. Therefore the last two digits must be divisible by 19

Of the 5 possible 2 digit numbers divisible by 19 (19,38,57,76,95), we can eliminate 19 and 95 as there exists no first digit to give such a number digits that are strictly increrasing or strictly decreasing as required by Q4.

Similarly we can eliminate 76 as it (when spelled out) contains both x and v which would leave Q7 with two correct answers. In the same manner we can eliminate 38 as the two possible numbers ending in 38 with strictly ascending digits (138 and 238) would leave question 7 with no answer at all.

This leaves us with a 3 digit number ending in 57. No number ending in 57 can be divisible by either 2 or 5 so Q3 indicates tht it must be divisible by 3. The only 3 digit number with strictly increasing digits that ends in 57 and is divisible by 3 is 357

Therefore 357 is the answer

Posted by FatBoy on 2003-09-04 08:39:46