Working Backwards
A person comes into a store and says to the shopkeeper, “I will buy half of your eggs plus half of an egg.” The transaction is made. A second person comes into the store and makes the same transaction. So does a third. The shopkeeper notices that he now has one egg left. How many eggs did he begin with?
15 eggs
There is a family in which each boy has as many sisters as brothers.
But each of the girls has twice as many brothers as sisters.
How many girls and boys are in the family?
4 boys, 3 girls
A ship left San Diego at 9:00 a.m. going 10 miles per hour on a course set for Hawaii. Another ship left San Diego at noon on the same course going 15 miles per hour. At what time did the second ship overtake the first ship?
How many miles were they from San Diego?
At 6:00 p.m. the second ship overtook the first ship; both ships were 90 miles from port.
The most popular two digit number is....
13
This year my teacher read us the book The Phantom Tollbooth, and since then I’ve been having strange dreams about driving in unusual places and paying tolls to unusual characters. Last night I dreamed about a highway in the clouds near the mythical Mt. Olympus. At my first tollbooth a mythical goddess asked for one-half my gold pieces plus two more. At the next tollbooth, a Greek hero demanded one-half my remaining gold pieces plus two more. Then at a third booth, Zeus himself asked me for one-half my remaining gold pieces plus two more. As I approached another tollbooth I began to worry that I wouldn’t have enough gold pieces for all the tollbooths. I wondered what they did to people without enough gold pieces. I looked in my purse and noticed I only had four gold pieces left. I was really beginning to worry, when my mom woke me up by calling me to breakfast. How many gold pieces did I start with in this dream?
60 gold pieces
A farmer must get three chickens and three sheep safely across a river. (The farmer cannot cross.) There is a raft that can carry up to three animals, and at least one animal, either a chicken or a sheep, must be on the raft at all times until all animals have reached the other side safely. However, it is not permissable for the sheep to out number the chickens either on the raft or on the shore.
What is the smallest number of trips needed to make the crossing?
S S S, S, C C C, C, C S
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
11 cartons total
How many seconds in 6 weeks
3,628,800 seconds
Blake gave one-half of his marbles to Isabel. Then he gave two-thirds of the remaining ones to Olivia. If he ended up with 10, how many did he have when he started?
60 marbles
The Oyster River Basketball team took 22 people to the ball game. Three people rode to the game in each car, and seven people took the bus. On the way home, four people rode in each car, and the rest took the bus. How many people took the bus on the way home?
2 people
A duck was given $9, a spider was given $36, and a bee was given $27. Based on this information, how much money would be given to a cat?
$18
In Asia, what number is considered UNLUCKY?
4
Yash owns one-half of a business. He sells one-fourth of his holdings for $12,500. What was the value of the business?
$100,000
How many different ways can Kylie, Julia, and Jack line up, single file, at the drinking fountain?
6 different ways
If it took 6 people 9 hours to build a barn, how long would it take 12 people to build the same barn?
None because the barn is already built
(6 × 9) + (6 + 9)
(6 × 9) + (6 + 9) = 69
On their way to the Oyster River High School Soccer Finals, Devon, Sam, and Kylie each took turns driving. Kylie drove 35 miles more than Sam. Sam drove four times as far as Devon. Devon drove 20 miles. How many miles did they drive total?
215 miles
Shriram has three stacks of 18 donuts. The first stack has three more donuts than the last stack. The last stack has six fewer than the second stack. How many donuts are in each stack?
First stack, six; second stack, nine;
third stack, three.
Using only addition, how can you add eight 8’s to get the number 1,000?
888 +88 +8 +8 +8 =1,000
My twin lives at the reverse of my house number. The difference between our house numbers ends in two. What are the lowest possible numbers of our house numbers?
The lowest possible numbers for the houses are 19 and 91. The difference is 72.