PRACTICAL ACTIVITIES INPRACTICAL ACTIVITIES INPROBLEM SOLVINGPROBLEM SOLVING

WEEK 3WEEK 3

DUCKS & COWSDUCKS & COWS

Activity 1.2Activity 1.2 DeakinDeakin University Study GuideUniversity Study Guide–– Farmer McDonald raises ducks and cows.Farmer McDonald raises ducks and cows.

The animals have a total of 9 heads and 26The animals have a total of 9 heads and 26feet. How many ducks and how many cowsfeet. How many ducks and how many cowsdoes Farmer McDonald have?does Farmer McDonald have?

–– What if there wereWhat if there were9 heads and 20 feet9 heads and 20 feet10 heads and 24 feet10 heads and 24 feet6 heads and 17 feet6 heads and 17 feet

DUCKS & COWSDUCKS & COWS

Activity 1.2Activity 1.2 DeakinDeakin University Study GuideUniversity Study Guide–– If Farmer McDonald sees some kind ofIf Farmer McDonald sees some kind of

animal and altogether sees 24 feet (notanimal and altogether sees 24 feet (notincluding his own), how many ducks andincluding his own), how many ducks andcows does farmer McDonald see? Show allcows does farmer McDonald see? Show allpossible answers.possible answers.

Missing FishMissing Fish

•• Two fathers took their sons fishing.Two fathers took their sons fishing.

•• Each man and son caught one fish, butEach man and son caught one fish, butwhen they returned to camp there werewhen they returned to camp there wereonly 3 fish. How could this be?only 3 fish. How could this be?

(None of the fish were eaten,(None of the fish were eaten,lost, or thrown back.)lost, or thrown back.)

Make the Number 100

Using the numerals 1,7,7,7 and 7 (a "1"and four "7"s) create the number 100.

As well as the five numerals you can usethe usual mathematical operations +, -,x, ÷ and brackets ( ).

For example: (7+1) × (7+7) = 112 wouldbe a good attempt, but not right,because it is not 100.

CensusCensus A census taker approaches a house and asks theA census taker approaches a house and asks the

woman who answers the door, "How manywoman who answers the door, "How manychildren do you have, and what are their ages?"children do you have, and what are their ages?"

Woman: "I have three children, the product ofWoman: "I have three children, the product oftheir ages are 36, the sum of their ages are equaltheir ages are 36, the sum of their ages are equalto the address of the house next door."to the address of the house next door."

The census taker walks next door, comes back andThe census taker walks next door, comes back andsays, "I need more information."says, "I need more information."

The woman replies, "I have to go, my oldest childThe woman replies, "I have to go, my oldest childis sleeping upstairs."is sleeping upstairs."

Census taker: "Thank you, I now have everything ICensus taker: "Thank you, I now have everything Ineed."need."

What are the ages of each of the three children?What are the ages of each of the three children?

The Lazy GardenerThe Lazy Gardener

It takes two gardeners 8 days to mow a lawn. One isIt takes two gardeners 8 days to mow a lawn. One islazy and one is energetic. The energetic one wouldlazy and one is energetic. The energetic one wouldonly take 12 days to mow it on his own. How manyonly take 12 days to mow it on his own. How manydays would the lazy gardener take to mow the lawndays would the lazy gardener take to mow the lawnon his own?on his own?

Housing PuzzleHousing Puzzle

Ali lives besideAli lives beside BalanBalan but not beside Chan.but not beside Chan. Danny lives in the second house on the left.Danny lives in the second house on the left. BalanBalan lives somewhere between Eliza and Chan.lives somewhere between Eliza and Chan. Danny lives beside Eliza.Danny lives beside Eliza.

There are five houses along one side of a street.There are five houses along one side of a street.

H1 H2 H3 H4 H5

Use the clues to work out who lives in the middle house.Use the clues to work out who lives in the middle house.

The Hourglasses PuzzleThe Hourglasses Puzzle

You need to boil eggs for exactly 9You need to boil eggs for exactly 9minutes, or else the visiting Duchess willminutes, or else the visiting Duchess willcomplain, and you will lose your job ascomplain, and you will lose your job ashead chef.head chef.

But you have only 2 Hourglasses, oneBut you have only 2 Hourglasses, onemeasures 7measures 7--minutes, and the otherminutes, and the othermeasures 4measures 4--minutes. How can youminutes. How can youcorrectly measure 9 minutes?correctly measure 9 minutes?

EGG FIASCOEGG FIASCODallas had a job at the egg packing plant. Out of oneDallas had a job at the egg packing plant. Out of onecrate of eggs yesterday morning, Dallas dropped thecrate of eggs yesterday morning, Dallas dropped thefirst two dozen eggs as they were being moved intofirst two dozen eggs as they were being moved intothe packing line. Half of the remaining eggs werethe packing line. Half of the remaining eggs werediscoloureddiscoloured and donated to the food bank. Half of theand donated to the food bank. Half of theremaining eggs didn't pass size inspection and wereremaining eggs didn't pass size inspection and weremoved into the commercial cooking line. Half of themoved into the commercial cooking line. Half of theeggs that were left were cracked and had to beeggs that were left were cracked and had to bedisposed of.disposed of.If Dallas had only 7 eggs left, how many eggs wereIf Dallas had only 7 eggs left, how many eggs wereoriginally in the crate?originally in the crate?

TOADS AND FROGS PUZZLETOADS AND FROGS PUZZLE

TOADS AND FROGS PUZZLETOADS AND FROGS PUZZLE

Mathematicians???

Three men are in a hot-air balloon. Soon, they findthemselves lost in a canyon somewhere. One of thethree men says, "I've got an idea. We can call for help inthis canyon and the echo will carry our voices far." So heleans over the basket and yells out, "Helllloooooo!Where are we?" (They hear the echo several times).

15 minutes later, they hear this echoing voice:"Helllloooooo! You're lost!!"

One of the men says, "That must have been amathematician." Puzzled, one of the other men asks,"Why do you say that?"

The reply: "For three reasons. (1) he took a long time to answer, (2) he was absolutely correct, and (3) his answer was absolutely useless."

Mathematics JokesMathematics Jokes

There are three kinds of mathematicians: thoseThere are three kinds of mathematicians: thosewho can count and those who cannot.who can count and those who cannot.Q.Q. Did you hear the one about the statistician?Did you hear the one about the statistician?A.A. Probably....Probably....My geometry teacher was sometimes acute, andMy geometry teacher was sometimes acute, andsometimes obtuse, but always, he was right.sometimes obtuse, but always, he was right.Old mathematicians never die; they just loseOld mathematicians never die; they just losesome of their functions.some of their functions.A statistician can have his head in an oven andA statistician can have his head in an oven andhis feet in ice, and he will say that on thehis feet in ice, and he will say that on theaverage he feels fine.average he feels fine.