Bonus problems (2009–2010)
Here are the bonus problems that I have given so far this year. You can submit answers up to the time when I post the solution on the solutions page. You can discuss the problem with whoever you want, but answers must be submitted in your own handwriting. It is not enough to submit a number as your answer. Some explanation of how you solved it must be provided as well.
Speeding to Aunties House (10/9/09)
Joe is traveling to his Aunt’s house in another state. For the first half of the distance he averaged 50 kph (kilometers per hour). If he wants his average speed for the trip to be 80 kph, how fast (on average) does he have to drive for the second half of the distance?
[hint: It does not say how far it is to his Aunt’s house so assume something simple like 100 k]
Great Discount on Coat (10/16/09)
A coat is discounted 20%, then another 20% then another 20%. If it had been originally discounted to its final price, what percent would the discount have been?
Dried Apples (10/23/2009)
You have 10 kilograms of apples. You are told they are 98% water. After leaving them outdoors for 2 days, you are told they are now 96% water. How much do the dehydrated apples weigh?
Nuclear Explosion (10/30/2009)
After a nuclear explosion there is a deadly amount of radiation in the air. The amount of radiation decreases by 1/2 every 2 days. If initially the radiation is measured at 2000 roentgens, how long must a survivor wait before they can safely leave the bomb shelter if a safe level of radiation is considered to be anything less than 9 roentgens?
Making Moonshine (11/13/2009)
Joe makes moonshine from barley. Joe keeps 10% of the moonshine produced as payment for his work. If Skip gets 1 liter of moonshine for the barley he brought Joe, how much moonshine did his barley make?
Jungle Animals in a Cage (12/11/2009)
There is a cage at the zoo that holds different jungle animals. In the cage are 11 heads and 20 feet. There are twice as many jungle creatures with 4 feet as those with 2 feet. How many of each type are in the cage?
[hint: not everything in the cage has to have 4 feet or 2 feet.]
Fishing Pole (1/8/2010)
A child who bought a 5-foot fishing pole wants to get on a bus. The bus driver says “sorry you cannot bring on anything longer than 4 feet”. The boy goes back in the store and gets something else that allows him to bring the fishing rod on the bus. What did he get? Note: he does not bend or dismantle the 5 foot rod.
Men Eating Cakes (1/15/2010)
If a man and a half can eat a cake and a half in a minute and a half, how many men would it take to eat 60 cakes in 30 minutes?
Burning Fuses
A man has two fuses that burn for exactly 30 seconds each, but not necessarily at continuous rates of speed. How can he burn the fuses to measure exactly 45 seconds?
More Boys or Girls?
In a certain country a law was passed that a married couple can have as many girls as they want, but have to stop having children after they have one boy. After 10 years will there be more boys than girls or more girls than boys? Explain.
Sharing Birthdays
If there are 10 people in a room, what is the probability that two of them share the same birthday?
Painting a Fence
Jill can paint a fence in 2 hours. To paint the same fence, Bob would take 3 hours. How long will it take them if they paint at the same time?
Collecting Baseball Cards
Dad and Junior collect baseball cards. Last year when Dad had 40 cards, he had twice as many as Junior. By the time his (Junior’s) birthday arrived, Junior had doubled his collection. Junior then got 1/6-th of Dad’s collection, and now has 51 cards. Then Sister suggests that Dad give Junior enough cards to make their collections equal. How many cards should Dad give?
Chimps Alfred and Betty
The combined ages of chimpanzees Betty and her child Alfred is 105 years. Betty is twice as old as Alfred was when Betty was as old as Alfred is now. How old are they?
Chickens and Eggs
If 5 chickens can lay 7 eggs in 2 days, how many eggs could 7 chickens lay in 20 days?
Circles and Lines
Point A marks the center of the circle to the right. Point B is 4 inches from A. Points ABCD mark the corners of a rectangle. Point E is 6 inches from B. How long is line BD?
Pizzas for Wine
Gino and Gweedo want some dandelion wine. At the end of a day of picking dandelions, Gino had picked 5 bushels and Gweedo had picked 3. Next, they stopped at their friend Fanuchi’s since he promised to make them pizzas in exchange for 1/3 of the dandelions picked. Not sure of the best way to split the eight bushels of dandelions, they put them into 24 baskets and each kept 8. In exchange for the 8 baskets that Fanuchi got, he baked them 8 pizzas. Gino said he deserved more because he picked more bushels. How should the pizzas be divided fairly between Gino and Gweedo?
Counterfeit Coins
There are 10 bags of coins. One of the bags contains all fake coins. The fake coins weight 11 grams and the real coins weigh 10 grams. There are 100 coins in each bag. How can you determine which bag has the counterfeit coins if you are allowed to make only a single weighing on a scale?
Missionaries and Cannibals
Three missionaries and three cannibals must cross a river using a boat which can carry at most two people. For both banks, if there are missionaries present on the bank, they cannot be outnumbered by cannibals (if they were, the cannibals would eat the missionaries.) The boat cannot cross the river by itself with no people on board. How can they cross? How many trips will it take?
Houses and Utilities
You have 3 houses and 3 utilities. You need to draw a line that connects each house to each utility. None of the lines can touch. The lines need not be straight and the surface need not be flat. Can you do it?