1. What's My Rule?

1A. IN 1 2 3 4 5 6 7 8 9 (Hint: Spell out the numbers)

OUT 3 3 5 4 4 3 5 5 4

1B. IN 1 2 3 4 5 6 7 8 9

OUT O T T F F S S E N

1C. IN 1 2 3 4 5 6 7 8 9 10 11 12

OUT 31 29 31 30 31 30 31 31 30 31 30 31

2. Which number comes next in the sequence?

2A. 3, 5, 7, 9, 11, 13, 15, 17, 19, ?

2B. 3, 5, 7, 11, 13, 17, 19, ?

2C. 2, 5, 10, 17, 26, 37, 50, 65, 82, ? (Hint: Think instead
about 1, 4, 9, 16, 25, ...)

2D. 1, 2, 4, 8, 16, 32, 64, 128, ?

3. Alphametics (Substitute a unique digit for each letter - these are
hard without hints for several letters)

3A: WYOMING x 8 = ILLINOIS

3B: FLORIDA x 5 = OKLAHOMA (Hint: There are just
2 possible digits for A)

3C: AB x C = DE and FG - DE = HI (Don't use 0 in the solution)

4. Digits in dates - Assume dates are written mm/dd/yyyy with no leading
zeros and the date is 3/7/2000

4A. What was the last date which had all odd digits?

4B. What is the next date which will have all odd digits?

4C. What was the last date which had all even digits?

4D. What is the next date which will have all even digits?

4E. What is the next date which will alternate odd and even digits
starting with an odd digit?

5. Counting and spelling - Spell out the numbers starting with
1 (Example: 41 = forty one)

5A. What is the first number whose spelling includes the letter "a"?

5B. What is the first number whose spelling includes the letter "n"
7 times?

6. Probability - Assume you have a multiple choice test with 40 problems
and 4 choices per problem.

6A. How many problems would you expect to get correct on average if
you guessed on each problem?

7. Change for a dollar - "I need to make a phone call, and all I have
is a dollar bill," said George. "Can you make change for a dollar?"
"Sure," replied Susan, rummaging through her purse. "Hmm. I have
more than a dollar, but I can't give you exact change."

7A. How much money could Susan have in pennies, nickels, dimes, and
quarters and still not be able to make exact change for a dollar?
**Source: Discover (magazine) Oct-1999, page 119 (Scott Kim's Bogglers
column)**

8. Math League contests (5th through 8th grade)
**Source: The Math League contest problem books - http://www.mathleague.com**

9. Problems of the week (elementary school and middle school)
**Source: The Math Forum - http://forum.swarthmore.edu**

Don Braffitt

1A. OUT is the number of letters in the spelling of IN

1B. OUT is the first letter of the spelling of IN

1C. OUT is the number of days in each month for a leap year

2A. 3, 5, 7, 9, 11, 13, 15, 17, 19, 21
(odd numbers)

2B. 3, 5, 7, 11, 13, 17, 19, 23
(odd prime numbers)

2C. 2, 5, 10, 17, 26, 37, 50, 65, 82, 101 (squares+1 - 1+1, 4+1, 9+1,
16+1, 25+1, ...)

2D. 1, 2, 4, 8, 16, 32, 64, 128, 256
(double previous number; powers of 2)

3A. WYOMING x 8 = ILLINOIS
7920658 x 8 = 63365264

3B. FLORIDA x 5 = OKLAHOMA 8741290
x 5 = 43706450

3C. AB x C = DE and FG - DE = HI 17 x 4
= 68 and 93 - 68 = 25

4A. What was the last date which had all odd digits?
11/19/1999

4B. What is the next date which will have all odd digits?
1/1/3111

4C. What was the last date which had all even digits?
2/28/2000

4D. What is the next date which will have all even digits? 4/2/2000

4E. What is the next date which will alternate odd and even digits
starting with an odd digit? 1/2/3010

5A. What is the first number whose spelling includes the letter "a"?
one thousand

5B. What is the first number whose spelling includes the letter "n"
7 times? nine hundred ninety nine

6A. 10 problems out of 40 (25% or 1 problem out of 4)

7A. 3 quarters, 4 dimes, and 4 pennies = $1.19

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