Each of the 14 questions below is answered by a different whole number from 1 to 14. Can you figure out which number goes with each question?
- How many of these questions have an answer that isn't a perfect square?
- How many of these questions, if their answers were considered atomic numbers,
would represent elements that end in the letter M?
- How many of these questions have an answer that couldn't be the length of one side of a right triangle, if each side's length is an integer from 1 to 15?
- How many of these questions have an answer that could be the third side of a
triangle if the other two sides' lengths are 8 and 10?
- How many of these questions have an answer that divides evenly into 27,720?
- How many of these questions have an answer that divides evenly into another
answer?
- How many of these questions have an answer that divides evenly into the sum of all the answers?
- How many of these questions have an answer that, if converted to a binary number,
is not a palindrome?
- How many of these questions have an answer that is a rational number?
- How many of these questions have an answer that is a perfect cube?
- How many of these questions have an answer that is a perfect number?
- How many of these questions have an answer that is both an odd prime and less than the
average of all the answers?
- How many of these questions have an answer that is divisible by 2 or 7?
- How many of these questions have an answer whose factorial ends in 0?
Solution to the Problem:
a | 11 | All except 1, 4, and 9 | ||
b | 6 | 2 (Helium), 3 (Lithium), 4 (Beryllium),
11 (Sodium), 12 (Magnesium), and 13 (Aluminum) | ||
c | 5 | 1, 2, 7, 11, and 14 | ||
d | 12 | All except 1 and 2 | ||
e | 13 | All except 13 | ||
f | 7 | 1, 2, 3, 4, 5, 6, and 7 | ||
g | 4 | 1, 3, 5, and 7 | ||
h | 9 | 2, 4, 6, 8, 10, 11, 12, 13, and 14 | ||
i | 14 | |||
j | 2 | 1 and 8 | ||
k | 1 | 6 | ||
l | 3 | 3, 5, and 7 | ||
m | 8 | 2, 4, 6, 7, 8, 10, 12, and 14 | ||
n | 10 | 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14 |
Also, thanks to Larry Schwartz for pointing out the error for clue C.
Originally, Question c. stated "How many of these questions have an answer that couldn't be
the length of one side of a right triangle, if each side's length is an
integer?" Larry wrote that "All integers from 3 to 14 could be a side of a right triangle:
3 4 5
6 8 10
7 24 25
9 12 15
11 60 61
5 12 13
14 48 50
Correctly solved by:
1. Sagar Patel |
Brookstone School Columbus, Georgia |
2. Jeff McKenzie | John Handley High School Winchester, Virginia |
3. Andrew Dau | South O'Brien High School Gaza, Iowa |
4. Magdy Essafty | Alexandria, Egypt |
5. Mike Singer | John Handley High School Winchester, Virginia |
6. Larry Schwartz | Norwalk, Connecticut |
7. Sharina Smith | Newport News, Virginia |
8. Tristan Collins | Virginia Tech Blacksburg, Virginia |
9. Billy Sutherland | John Handley High School Winchester, Virginia |
10. Garrett Hix | Brookstone School Columbus, Georgia |
11. Danny Gordon | Brookstone School Columbus, Georgia |
12. Julianne Harris | John Handley High School Winchester, Virginia |
13. Maggie Morrison | John Handley High School Winchester, Virginia |
14. David & Judy Dixon | Bennettsville, South Carolina |
15. Andrew Montoya | John Handley High School Winchester, Virginia |
16. Ben Bassett | Sewell, New Jersey |
17. Kelley Kolar | John Handley High School Winchester, Virginia |
18. Emily Stapp | Mountain View High School Mountain View, Wyoming |