1. Rumpelstiltskin A Math Problem
By Jacqui McLellan

2. Table of Contents
Events- pg 3, pg 5 Outcomes- pg 3, pg 8 Pascal’s Triangle- pg 28/29 Permutations- pg 11 Combinations- pg 8, pg 23 Trials- pg 5 Theoretical probability- pg 3 Experimental probability- pg 5 Independent events- pg 17 Subsets- pg 5 Complimentary events- pg 3 Counting techniques- pg 5, pg 8, pg 11, pg 13, pg 23 Sample space- pg 5

3. Once upon a time there was a poor miller who had a beautiful daughter
Once upon a time there was a poor miller who had a beautiful daughter. The miller was very proud of her looks and her brains. Q1
If the miller has genes for recessive blonde hair (bb) and the millers wife has brown hair (Bb) then what is the probability that their daughter has blonde hair? Brown?

4. One day the miller was out for a walk when he spotted to king and his company, he bowed graciously. He and the king began to chat and the miller stupidly boasted to the king, "My daughter can spin straw into gold." The king was shocked, “If your daughter can do this," said the king, "bring her to me and I shall see."

5. So the miller went home and told his daughter to wear her most lovely dress and come before the king. Q2
The daughter has a choice between 3 dresses; one blue strapless, one white with a bow, and one yellow sun dress. Roll 2 die 50 times and record the outcomes if blue=1,2 white=3,4 and yellow=5,6. Which dress does she chose? What is the sample space avaliable?

6. The millers daughter entered the castle and her arrival was announced to the king. The king took the girl to a room in the dungeon of his castle that was filled to the brim with straw. As he showed her the spinning wheel in the corner he said, “Spin this straw into gold by sunrise or you shall die.” And walked out of the room slamming the door shut.

7. After trying the door – which was locked – and all the windows – which were barred - the woodcutter's daughter sat on the stool and began to cry. Suddenly, the door creaked open and a strange little man appeared.

8. "What will you give me to spin this straw into gold
"What will you give me to spin this straw into gold?" asked the little man.
"I'll gladly give you my necklace."
"Good," he said taking the necklace. Q3
If the millers daughter has three chains each and each can hold 3 gems has 12 gems to choose from how many possible combinations are there when order DOESN’T matter? Make a list of the possible outcomes.
The little man set to work and by sunrise the room was filled with gold.

9. When the king saw the gold he became greedy. He got more straw
When the king saw the gold he became greedy. He got more straw. “By sunrise all this shall be gold.”

10. Once more the miller’s daughter began to cry
Once more the miller’s daughter began to cry. In that moment the door opened and in came the strange little man still wearing her necklace.

11. Q4 “I'll gladly give you my ring,” said the girl.
“What will you give me this time?” he asked.
“I'll gladly give you my ring,” said the girl.
“Good,” said the little man as he sat down to spin the straw. Q4
If the daughter has 2 rings, one gold one silver, each with 4 settings to place a stone and 8 different stones to place, what is the sample space? How many possible combinations are there when order DOES matter?

12. By sunrise all the straw was gold. Once more the king was pleased
By sunrise all the straw was gold. Once more the king was pleased. He got even more straw.

13. “Spin this straw into gold and in the morning I shall marry you and make you my queen.”
The king (AKA the most eligible bachelor in the land) has 4 perspective wives (the bakers daughter, the butchers daughter, the candlestick makers daughter and the millers daughter). One of these girls he will marry, one his brother will marry, one he will give a large sum of money to and one who will walk away with nothing. Using box technique or factorial notation what is the probability that the candlestick makers daughter will be married to the brother of the king.

14. When the king went away the little man returned wearing both the necklace and the ring. "What will you give me this time?" he asked.

15. "I've nothing left to give," replied the miller's daughter sadly
"I've nothing left to give," replied the miller's daughter sadly. "Then you shall give me your first child when you are queen." She promised the little man her first child.

16. And when the king came in the morning, and found all as he had wished, he took her in marriage, and the pretty miller's daughter became a queen. The happy queen had a baby boy and forgot all about her promise.

17. On the day of the little boys first birthday the little man came to collect his payment.Q6
At the little boys party there is a magician. The magician has a deck of cards and a die. He rolls the die and pulls out a card. When he pulls out an ace what is the probability of him rolling a 4? What kind of an event is this?

18. The queen was horror-struck, and offered the little man all the riches of the kingdom if he would leave her the child. But the little man said, "No, something alive is dearer to me than all the treasures in the world."

19. Then the queen began to lament and cry, causing the little man to pity her. So the little man made her a deal. “If you can guess my name in three days time I shall let you keep your little boy.”

20. James Alex Rob John Napoleon
All night the queen thought of every name. In the morning when the little man came she tried all of them. At each one the little man said, "No. It is not I."
James
Alex
Edward
Rob
John
Napoleon

21. On the second day she tried even more names. "No
On the second day she tried even more names. "No. It is not I," said the little man.

22. That night one of the queen's messengers came to her to tell of a strange sight indeed.
While riding through the forest he had seen a fire. Around the fire danced a little man who sang a song. This was what he sang:

23. "Today I bake, tomorrow I brew, Then, dear prince, I come for you
"Today I bake, tomorrow I brew, Then, dear prince, I come for you. None can guess, none can claim That Rumpelstiltskin is my name." Q7
Rumpelstiltskin is a long word, so is supercalafragalisticexpialadotious. How many combinations of letters can you make out of supercalafragalisticexpialadotious?

24. That night the little man came calling. "What is my name
That night the little man came calling. "What is my name?" he asked, jumping up and down.

25. "It's Robin," answered the queen.
“NO!”

26. "It's Jack," said the queen.
“NO!”

27. "Then Rumpelstiltskin is your name
"Then Rumpelstiltskin is your name." At this the little man flew into a rage.

28. "The devil told you that, the devil told you that
"The devil told you that, the devil told you that!” he shrieked, and stamped his feet so hard that he fell through the floor and disappeared forever. Q8
Using Pascal’s Triangle, how many different ways can you spell Rumpelstiltskin?

29. R U U M M M P P P P E E E L L L S S T T T I I I I L L L L L T T T T S S S S S K K K K K K I I I I I N N N

30. The End