Problem of the Week #19: February 25th, 2008

Grade 6:

Tommy and Sally have a box of cookies that they plan to share with three friends. Tommy and Sally discover that they number of cookies cannot be divided evenly among the five of them.
Tommy says “ If we eat one cookie the number left will make an even number of cookies for everyone.”
Sally says “ If you and I take two less cookie than our friends, then they can each have seven cookies with none left over.”
How many cookies were in the box?



Grade 7: Allowance
Miles receives a weekly allowance of $8. He can earn $5 more for each special job he completes beyond the usual chores. In twelve weeks, Miles wants to have saved enough to buy a video game player that costs $210. If he saves all of his money, how many special jobs does he need to complete to earn what he needs?



Grade 8: Shipping Cartons
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. The boxes are never mixed in a carton. 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?

Grade 9: 999 Coins
Starting with a single pile of 999 coins, a person does the following in a series of steps: In step one, he splits the pile into two nonempty piles. Thereafter, at each step, he chooses a pile with 3 or more coins and splits this pile into two piles. What is the largest number of steps that is possible?
Grade 10: Multiples of Four - February 2008
How many multiples of four from 1 through 1000 do not contain any of the digits 6, 7, 8, 9, or 0?