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Problem
Solving Strategy |
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Solution |  |
1. Mr Green has a small farm near Steinbach, Manitoba. He has chickens and cows on his farm. If there are 32 legs altogether, what is the greatest number of cows possible?
Always maintain a constant total of 32 legs in total.
If all the legs belong to cows only, then 8 cows (32�4) are possible.
But there must be at least 1 chicken on the farm.
Exchange 1 cow for 2 chickens.
| Chickens | Cows | Legs |
| 0 | 8 | 32 |
| 2 | 7 | 32 |
There are at most 7 cows.
2. List the different combinations of 5-� coins and 10-� coins that make 55�.
| 5-� coins | 11 | 9 | 7 | 5 | 3 | 1 |
| 10-� coins | 0 | 1 | 2 | 3 | 4 | 5 |
As there must be at least 1 coin of each, only 5 different combinations exist.
3. Each time 2 dice are rolled, 2 numbers land flacing up.
A) How many different combinations of numbers can there be?
Hint: Only count different sets of numbers. Example: 1, 3 and 3, 1 are the same.
B) How many different products can there be?
| Dice Pair |
x | Dice Pair |
x | Dice Pair |
x | Dice Pair |
x | Dice Pair |
x | Dice Pair |
x | No. | 21
different |
| 11 | 1 | 22 | 33 | 9 | 44 | 16 | 55 | 25 | 66 | 36 | 6 | ||
| 12 | 2 | 23 | 34 | 45 | 20 | 56 | 30 | 5 | |||||
| 13 | 3 | 24 | 8 | 35 | 15 | 46 | 24 | 4 | |||||
| 14 | 4 | 25 | 10 | 36 | 18 | 3 | |||||||
| 15 | 5 | 26 | 12 | 2 | |||||||||
| 16 | 6 | 1 | |||||||||||
| No. | 6 | 3 | 3 | 3 | 2 | 1 | |||||||
| 18 different products | |||||||||||||
4. In a box there are twelve pieces of paper, each with a number. The first is numbered 1, the second 2, the third 3, and so on until 12. The box is shaken and the numbers drawn out in pairs. If the sums for each of the six pairs are 4, 6, 13, 14, 20, and 21, what are the numbers that make up the pairs?
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
| 4 | / | / | |||||||||||
| 6 | / | / | |||||||||||
| 13 | * | / | / | * | |||||||||
| 14 | / | * | * | / | |||||||||
| 20 | / | / | |||||||||||
| 21 | / | / |
Legend:
| / | Actual pair selected |
| * | Alternative pair rejected |
5. Sally is having a early. The first time the doorbell rings, one person enters. If on each successive ring a group enters that has two more persons than the group thot entered on the previous wring, how many people enter on the sixth ring?
| Ring order | Person |
| 1 | 1 |
| 2 | 1 + 2 = 3 |
| 3 | 3 + 2 = 5 |
| 4 | 5 + 2 = 7 |
| 5 | 7 + 2 = 9 |
| 6 | 9 + 2 = 11 |
11 people enter on the sixth ring.
6. A kennel owner has the following dogs: a blonde collie, a brown terrier, a black poodle, a black collie, a blonde poodle, a while terrier, a brown collie, a black terrier, a while poodle, and a blonde terrier. If he wants to have one of each colour and breed combination, what types of dogs should he get?
| collie | terrier | poodle | |
| blonde | / | / | / |
| brown | / | / | ? |
| black | / | / | / |
| white | ? | / | / |
He should get a brown poodle and a white collie.
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