milagros317
Verified
- Joined
- Jan 12, 2002
- Messages
- 580,120
- Points
- 63
The following math puzzle seems to have too little information to be solved, but that is not the case. There is a unique minimal solution to all the questions at the end.
Susan is a child who hates pennies. She hates pennies so much that she will neither receive any in change nor possess any to give to any cashier. Instead she refuses to buy any collection of items that would involve giving or receiving pennies. For example, if the total charge is $1.28, she will refuse to make the purchase because she would have to receive two pennies in change or hand over three pennies.
Susan loves candy of all kinds. She has some US coins in her pocket. Of course, she has no pennies among them. [For those not familiar with US coins, they are in denominations of 1, 5, 10, 25, 50, and 100 cents. They are called, respectively, a penny (or a cent), a nickel, a dime, a quarter, a half dollar, and a dollar.]
Susan goes into a candy store. There are several jars of candy on the counter. All of the candies in any one jar are identical and have the same price.
Each jar contains a different type of candy at a different price from the other jars, and all the prices are a positive whole number of cents.
Susan asks the price of two candies from each of the jars. In every case, the total cost of two pieces would require her to hand over a penny besides using some of the coins in her pocket, so she refuses, even though she has more than enough money to pay.
Susan asks the price of three candies form each of the jars. In every case, she has coins that would pay for the three candies but she would receive one penny in change, so she refuses.
Susan then asks the price of one candy from each of the jars. To her delight, the total cost of one candy from each jar is an amount she can pay exactly with some of the coins in her pocket.
You now have enough information to answer all of the following questions:
1) What is the fewest number of jars of candy that there could be on the counter?
2) What are the lowest prices possible for the candies in each jar, listed lowest to highest?
3) What is the least total of amount of money that Susan could have in her pocket?
4) Presume that Susan has as few coins as possible to make all of the above true. Exactly what coins does Susan have in her pocket?
Susan is a child who hates pennies. She hates pennies so much that she will neither receive any in change nor possess any to give to any cashier. Instead she refuses to buy any collection of items that would involve giving or receiving pennies. For example, if the total charge is $1.28, she will refuse to make the purchase because she would have to receive two pennies in change or hand over three pennies.
Susan loves candy of all kinds. She has some US coins in her pocket. Of course, she has no pennies among them. [For those not familiar with US coins, they are in denominations of 1, 5, 10, 25, 50, and 100 cents. They are called, respectively, a penny (or a cent), a nickel, a dime, a quarter, a half dollar, and a dollar.]
Susan goes into a candy store. There are several jars of candy on the counter. All of the candies in any one jar are identical and have the same price.
Each jar contains a different type of candy at a different price from the other jars, and all the prices are a positive whole number of cents.
Susan asks the price of two candies from each of the jars. In every case, the total cost of two pieces would require her to hand over a penny besides using some of the coins in her pocket, so she refuses, even though she has more than enough money to pay.
Susan asks the price of three candies form each of the jars. In every case, she has coins that would pay for the three candies but she would receive one penny in change, so she refuses.
Susan then asks the price of one candy from each of the jars. To her delight, the total cost of one candy from each jar is an amount she can pay exactly with some of the coins in her pocket.
You now have enough information to answer all of the following questions:
1) What is the fewest number of jars of candy that there could be on the counter?
2) What are the lowest prices possible for the candies in each jar, listed lowest to highest?
3) What is the least total of amount of money that Susan could have in her pocket?
4) Presume that Susan has as few coins as possible to make all of the above true. Exactly what coins does Susan have in her pocket?