Hard Math Worksheets Name Answer Key_______
HMES
© 2013 Glenn Ellison
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13.1: Making Ordered Lists
1.
Word Problem: The accounts of ancient Egyptian poets indicate that Cleopatra died after
being bitten by an asp (also known as an Egyptian cobra). How many three letter English
words can you make by rearranging the letters in the word ASP? (Include ASP.)
3
2. List all two digit numbers that use only the digits 1, 3, and 5. Put the numbers starting with
1 first, then those starting with 3, then those starting with 5.
11, 13, 15, 31, 33, 35, 51, 53, 55
3. List all three digit numbers that use only the digits 0 and 1.
100, 101, 110, 111
4. List all three-letter sequences you can make using the letters A and D in the order that they
would appear in the dictionary. How many are English words?
AAA, AAD, ADA, ADD, DAA, DAD, DDA, DDD. Two are words.
5. At the start of a Scrabble game Adrienne had four A’s, a T, an N, and an O. She started the
game by making a two-letter English word. List all of the words that she might possibly
have made.
AA, AN, AT, NA, NO, ON, TA, TO
6. Suppose that Jack is taller than Kevin, who is taller than Penelope, who is taller than Kate.
Ms Cronin wants to pick one of four to be the narrator for a class play and one other to be
the director. She wants the director to be taller than the narrator. In how many ways can she
assign these two jobs?
6
7. Making Connections: How many three-digit prime numbers can be made using only the
digits 0 and 1.
1 (Only 101 is prime.)
8. Challenge: Suppose that there are five kids on the Cabot math team: Anna, Bob, Clarence,
David and Evelyn. The coach wants to choose three kids to go to a meet. Bob will only go
if David is also going. Anna won’t go if Clarence is going. David won’t go if he’s the only
boy. In how many ways can the team be chosen?
4 ways. (ABD, BCD, BDE, CDE)
Notes on 1: There are six arrangements. ASP, SAP, and SPA are words. On 4: ADD and
DAD are words. On 5: The question is a bit unfair in that the official Scrabble dictionary
includes many rarely used “words” including AA, NA, and TA in addition to the five more
normal words. (There are 13 two-letter sequences.) On 7: The connection is to sections 7.3
and 7.5. There are 4 possible numbers 100, 101, 110, and 111. Only 101 is prime. On 8:
One way is just to write out the 10 possible combinations and then cross out the ones that
violate each rule.