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Number Quiz (Posted on 2003-08-28) Difficulty: 3 of 5
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.)

  Submitted by Gamer    
Rating: 4.1111 (9 votes)
Solution: (Hide)
You figure that the answer must be 357, and mark 1)A, 2)A, 3)B, 4)A, 5)B, 6)A, 7)D, 8)C, 9)B, 10)A.

Looking at question 1, you see the number must be three digits, otherwise A and B would be true.

Looking at question 3 and question 6, you see that 6 must be answered A. If it was divisible by 20 (and the divisibility rules for 4 and 5 don't require any digits past the last 2), the answer to 3 would be A and C.

Looking at question 4 and question 6, you note the possible combinations for the number.

_19
_38
_57
_76
_95

You eliminate _19 and _95 because there is no possible first digit. Then from the remaining choices, 238 and 357 are the only ones that work for question 5, such that one of the choices there is right.

You see that two questions disallow 238 from being the answer. Question 7 and question 9 both have answers that aren't listed. Two hundred thirty eight has no J,L,Q,V,X, or Z, and only has two of the letter E. (Note: The word "and" doesn't matter at all in these spellings out.)

Since 357 works with all the questions, it is the number you picked to answer all the questions for.

Other methods for solving were posted in the comments.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle AnswerK Sengupta2022-06-03 00:06:43
SolutionSolutiontomarken2021-04-21 12:52:10
SolutionAnswerMath Man2015-08-25 19:14:12
re(2): SilverKnight, do not read this post......FatBoy2003-09-05 13:27:44
re: SilverKnight, do not read this post......SilverKnight2003-09-04 13:54:31
kudos to GamerFatBoy2003-09-04 09:06:06
SolutionSilverKnight, do not read this post......FatBoy2003-09-04 08:39:46
re(2): Note to GamerLawrence2003-08-30 00:45:33
re: Maximal Brute ForceGamer2003-08-30 00:07:15
re(2): Minimal Brute ForceDJ2003-08-29 22:57:43
Questionre: Minimal Brute ForceTalon50002003-08-29 17:02:59
re: educational guessDJ2003-08-29 16:00:26
re: educational guessCharlie2003-08-29 15:22:19
educational guesscobra2003-08-29 15:05:01
SolutionMaximal Brute ForceCharlie2003-08-29 08:57:40
Another stab at it.Lee2003-08-29 02:15:55
SolutionMinimal Brute ForceDJ2003-08-28 22:25:13
re: Note to GamerGamer2003-08-28 19:35:11
SolutionSame solution, deeper explanationnikki2003-08-28 19:18:14
Note to GamerLawrence2003-08-28 19:13:14
SolutionPop Quiz, Hot Shot ... what do you do?Lawrence2003-08-28 19:04:43
re: solutionviswam2003-08-28 18:11:18
Solutionsolutionviswam2003-08-28 18:09:41
Hints/Tips(2) re: some educated trial and error...Your buddy2003-08-28 18:05:53
Solutionsome educated trial and error...Your buddy2003-08-28 17:19:28
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