1.6 Self-Check for Unit 1
(a) The website you will go to has many sudoku puzzles. Pick just one or two to solve. Be mindful of your time and don’t spend more than 20 minutes on this activity, even if you enjoy solving sudoku puzzles. If you cross out lines and columns, use your math notebook as you do the steps. Then type your answers directly into the puzzle. The sudokus to select from are called “mini sudokus,” and they are in the third row of this sudoku collection. Try the 4×4. When you enter the, scroll down to access it.
(a) The sudoku puzzles from this page tell you if you filled them in correctly. When you have solved the 4 × 4 sudoku successfully, you can go on to the 6 × 6 version right next to it. The site saves your correct solution, so unfortunately you cannot ask another person to try this one from the same computer if you already filled it in correctly.
(b) In a dog park, there are 24 creatures (dogs plus people) present. Together, they have 80 legs. How many people and how many dogs were in the dog park?
(b) Eight people and 16 dogs make 24 creatures and legs.
You can go about this in different ways (and you may even have another way than the ones listed here).
Solution Idea 1: Draw a Picture
If 24 creatures have two legs each, we are using up 48 legs. There are 32 legs left over, which still have to be placed in the following (incomplete) picture:
Put two more legs with each of your bodies until you run out of legs:
This last picture now shows 16 dogs and eight people.
Solution Idea 2: Make an Educated Guess and Revise as Necessary
Make an educated guess: What if half of the creatures are people and half are dogs.
- 12 people have 24 legs
- 12 dogs have 48 legs.
- Together that makes 72 legs, which leaves us eight legs short.
- These eight extra legs make four two-legged creatures into four four-legged creatures. So we have four fewer people, but four more dogs.
- 12 people minus four people makes eight people.
- 12 dogs plus four dogs makes 16 dogs.
- There must have been eight people and 16 dogs
(You could have also continued your educated guesses as shown in the “New Vehicle” activity. For the revision you then use more dogs, since this will bring up the number of legs.)
Solution Idea 3: Use Pairs of Legs
- 80 legs make 40 pairs of legs, as .
- We are using 24 pairs of legs to give every creature two legs.
- 40 pairs of legs minus 24 pairs of legs leaves 16 pairs of legs left over.
- These 16 pairs are put with one creature each, which means each of these 16 creatures is a dog. 24 minus 16 is eight, so eight creatures only had one pair of legs, which is true for a person.
The answer is 16 dogs and eight people.