If a certain number of dogs and ducks have 30 heads and 100 feet, how many of each are there?
Set 04
Jacob’s Bumper
Jacob agreed to work at school for a year, doing odd jobs for Sam Daniels, the head custodian, for $240 and the front bumper of a 1958 T-bird (one of the custodian’s many relics from the history of the automobile). Jacob had to quit after seven months of the year were up. Mr. Daniels did some figuring and gave Jacob $100 plus the bumper. What was Mr. Daniels’ calculated value of the bumper?
Alex Watt’s Will (Scotland)
Alex Watt, piano maker and friend to man, died in Edinburgh, Scotland, in 1849. He left the contents of his vault as follows: half to his devoted wife Millie, one-tenth to his cousin Sam, one-fourth to Stella’s great-grandfather Angus, who moved to Amsterdam and married royalty, and the remaining 94 pounds to the Firth of Forth Bagpipe Band in Edinburgh, of which both he and Sam had been faithful members (Alex a piper, Sam on the bass drum). How much did Sam inherit?
Sum, Sum of Squares
I am thinking of two numbers. The sum of the numbers is 3; the sum of their squares is 29. What are the numbers?
Lookout Tower
Up in a forest fire lookout tower in California’s Sierra Nevada, Calvina and Carmela, the two watchers, need supplies. Three mules, led by ranch hand Jerry Milsaps, can carry supplies up to them. The mules are named Geranium, Delphinium, and Ammonium. Geranium can carry 200 pounds, Delphinium can carry 190 pounds, and Ammonium can carry 180 pounds. What supplies should each mule carry so that everything fits?
| Drinking water | 28 lb | Batteries | 61 lb | |
| Ice | 35 lb | Detective novels | 63 lb | |
| Kitty litter | 42 lb | Window glass cleaner | 77 lb | |
| Camera equipment | 44 lb | Ping pong table | 84 lb | |
| Back-up telescope | 48 lb | Mountain Dew | 88 lb |
False Coins 2 (9, Heavy, 2)
You are given nine gold coins, and one is heavier than the others. Can you find the heavier coin in only two weighings on a 2-pan scale?
Highland Island 1 (C, P)
On Highland Island, there are two tribes of natives, the Chocolates and the Peaches. Chocolates always, always tell the truth to any question they are asked, and Peaches always, always lie. Members of the two tribes all look pretty much alike—that is, there is no way to tell who belongs to which tribe just by looking. Therefore, life is rather confusing on the island, as you are about to discover.
You have been taking a walk and are on your way back to your campsite. You have come to a fork in the trail, and it is getting dark, and you don’t know which way to go, and you are hungry. There is a native sitting by the side of the trail, eating a banana. He will answer exactly one question for you. Think up ONE QUESTION to ask this person so that you will learn which trail will take you to your campsite. (You may assume that the native knows which is the correct trail.) If you figure out the right question to ask, the native might be pleased enough to share his banana with you. Good luck!
Burglary Witnesses
Six people, Anthony, Buzz, Chris, Deanna, Emily, and Fred, have witnessed a burglary and are trying to tell the police what the burglar (who got away) looked like. They disagreed a lot on what they’d seen. This is what they told the police.
| Witness | hair color | eye color | suit color | estimated age |
| Anthony | blond | blue | gray | 34 |
| Buzz | blond | black | dark blue | 30 |
| Chris | red | brown | dark brown | 34 |
| Deanna | black | blue | not dark brown | 34 |
| Emily | brown | black | gray | 28 |
| Fred | blond | brown | dark blue | 30 |
It turned out that, when the burglar was finally caught, each witness had been wrong on 3 of the 4 characteristics, but that each of the 4 characteristics had been identified correctly by at least one witness. Can you figure out what the burglar looked like?
Five Houses, Lemonade, Camel
There are 5 houses, each a different color and lived in by families of 5 different nationalities, with 5 different drinks, pets, and kinds of vehicles.
- The Dutch family lives in the white house.
- The Nigerian family owns the horse.
- The Indian family drinks tea.
- The lemonade drinkers have a dog.
- The gray house is the second house to the right of the yellow house.
- Coffee is drunk in the gray house.
- The car family lives just left of a Siamese cat.
- The bicycle belongs at the green house.
- Milk is drunk at the middle house.
- The Brazilian family lives in the first house on the left.
- The motorcycle is next door to the house with the dog.
- The bicycle is next door to the pet hamster.
- The moped driver drinks orange juice.
- The Canadian family has a van.
- The Brazilian family lives next door to the brown house.
Who drinks lemonade? Who owns the camel?
Path of Quarters
A quarter is 2.35 centimeters in diameter. If the race course for a 10-kilometer race is marked out with a continuous path of quarters, each one touching the next, and if you were to walk the race course and pick up all of the quarters, how much money would you have as you crossed the finish line? (What sort of a wheelbarrow would you need to have with you as you work your way along?)