3. 9. The numbers given are the first numbers that appear after the decimal point when converted from these fractions: 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, and 9/10.
4. 50. To get the next number in each step of this series, reverse the digits in the previous number, and then multiply them by 2.
5. ABC represent the numbers 1, 2, and 3. Multiply them together, and you get 6, the next step in the series. FGH represents 6, 7, and 8. Multiply them to get the next step: 336. CCFCCGCCH represents 336, 337, and 338. Multiply them to get the answer: 38272416.
6. SOAR and SORE
7. PAIL and PALE
8. BORE and BOOR
9. BAWL and BALL
10. FLUE and FLEW
11. Flib clop sca.
13. This method is of course not accurate to the exact millisecond, but it works: Lay the 2 strings out so that they are parallel and stretched all of the way out. There would have to be a few inches between them, but they should be as perfectly matched up side-by-side as possible. You light one string at both ends. It will burn out completely in 30 minutes. The exact point where it burns out - where the 2 flames from the 2 ends meet - you light that EXACT point on the other string, which is lying right next to the first string. You then quickly light both ends of the string. Now that string should be completely consumed in 15 minutes, for a total of 45 minutes. The point you light on the second string is crucial because it is the ACTUAL half way point of the string, as far as burn time goes. This is the answer submitted by a Puzz.com Puzzle Newsletter reader:
"A slightly more elegant solution to question 13 (the strings that must
burn in 45 minutes) and that allows for the strings NOT to be identical
(but still burn unevenly in 1 hour) is as follows:
Lay the two strings out so they don't touch. Light both ends of string
"A", and one end of string "B". When string "A" has burned out, exactly
30 min have gone by, which means that string "B" has exactly 30 min left
to burn. Light the other end of string "B". It will now burn out twice
as fast in exactly 15 min. The total burning time is 45 min."