2013-14 Problems

3rd and 4th graders

February, 2014

 
A.953. Sam and Tom are playing with 9 disks, which they numbered from 1 to 9. "Interesting! If I take this disk, I can arrange the rest of the disks into 3 groups so that the sum of the numbers of the disks in each group is the same." - said Tom. "Hey, I can arrange those 8 disks in 4 groups, also, so that your statement is true again." - said Sam. Which disk did Tom take out? Give an example for the 3 and the 4 groups.

A.954. Yummy took a walk to the black berry bushes. He picked 648 g of berries, but gave Smarty 2/3 of the berries, gave Funny 2/3 of the remaining berries, then gave Cuty 2/3 of the rest, and kept whatever he had left. How much black berries have left for Yummy?

A.955. Seven dragons live in Dragontown. Every dragon has a different number of heads, and the most heads the 7-headed dragon has. Every head on every dragon is numbered from 1 to whatever number is necessary to count every head on each dragon. The number on the head also indicates the number of teeth in that head. How many heads and how many teeth do the 7 dragons have all together?

A.956. Can you cut a triangle or a quadrilateral into more pieces with 3 straight lines? Describe the cuts with a diagram or otherwise.

A.957. A rectangular land is divided into 6 square shaped sections, as shown on the diagram. The side of the smallest square is 1 meter. How long is the side of the greatest square, e?
a957.gif

A.958. Replace the letters with digits, so that different letters mean different numbers, but the same letters mean the same numbers.
a958.gif

A.959. There are 3 trees in the garden. The 3 trees have a total of 360 kg of fruit on them. The apple tree and the pear tree together have twice as much fruit on them than the peach tree. The apple tree and the peach tree together have 60 kg more fruit than twice the fruit on the pear tree. There are 20 kg more peach than pear. How many kg of each fruit is there on each tree?

A.960. Create a magic 3x3 grid containing nine consecutive numbers so that the sum of the numbers in each column, row and diagonal is 2013.
 

Please, send your solutions here.

Junior Kindergarten  Grade 8  86 Fourth Ave. New York, NY 10003 (212) 475-5609  | Grades 9 – 12  46 Cooper Square New York, NY 10003 (212) 475-5610
Grace Church School is a co-educational independent school in downtown Manhattan, New York City
providing instruction for over 700 students in Junior Kindergarten through Grade 12.
Grace Church School © 2021