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 Number Quiz (Posted on 2003-08-28)
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.)

 See The Solution Submitted by Gamer Rating: 4.1111 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Solution | Comment 24 of 25 |
Interesting to see all the different approaches.  Here's how I did it:

From [3] we know it's divisibly by exactly one of 2, 3 and 5, so therefore from [6] we know that if you get rid of the number's first digit it is divisible by 19 (if the last two digits were divisible by 20 then the number would be divisible by both 2 and 5).

From [4] we know the digits are strictly increasing or decreasing, so the only possibilities are:

238, 357, 976

Applying either [7] or [9] from here rules out two choices and leaves 357 as the only possible number.

So questions 1, 2, 5, 8, 10 and one of 7 or 9 are unneeded.

 Posted by tomarken on 2021-04-21 12:52:10

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