Moving Day

July 16, 2018

The summer months are the most popular time to move to a new home. Janet’s family is moving, and she suddenly realizes just how much stuff they have in their current home. Once the moving company finishes packing everything in boxes, they begin the task of numbering them. A sticker is placed on every box and on every item that is too large to fit in a box. Janet notices that stickers in three distinct colors are used. There are blue stickers numbered 239 through 262, green stickers numbered 163 through 178 and yellow stickers numbered 453 through 492. How many total stickers were used by the packers?

Janet notices that the boxes numbered 238 through 245 contain all her belongings. She is pretty sure her MATHCOUNTS trophies are in the box numbered 242, which is a 12.5 × 12.5 × 17 box (measured in inches). What is the volume of this box, in cubic feet? Express your answer as a decimal to the nearest tenth.

Part of moving is remembering all the numbers associated with the new house, including a new phone number, new street address and new zip code. Janet can’t quite recall her new house number. What she knows for certain is that her new house number consists of three digits. The first digit is odd, the second is even and the third is odd. Janet also knows it is not a palindrome. How many different house numbers have all of these characteristics?