FOR CHILDREN

PROBLEM # 1
I have a miniature Pyramid of Egypt. It is 5  inches in height. I was invited to display it at an exhibition. I felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1/ 10) times the density of the material used for the miniature. I did a quick calculation to check whether the model would be big enough.

FOR GROWNUPS

PROBLEM # 2
The six terms 2x-3, t, 7-12y, x+3, 3y-4, x+12 are in arithmetic sequence. Find the ordered triple (x,y,t).

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SOLUTIONS TO PROBLEMS ON 06/01/06

FOR CHILDREN

PROBLEM # 1
Find the least positive integer such that when its leftmost digit is deleted, the resulting integer is 1/29 of the the original integer.

SOLUTION
725.

FOR GROWNUPS

PROBLEM # 2
Let N be the number of consecutive 0's at the right end of the decimal representation of the product 1!2!3!4!....99!100!. Find the remainder when N is divided by 1000.

SOLUTION
124.

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