Coin Stacks II

It is possible to mix coins in a stack to get a stack a whole number of millimeters high. For example, a stack of 2 nickels and 2 pennies has a height of exactly 2 × 1.95 + 2 × 1.55 = 7 mm. Can you find a stack of coins with a whole number of millimeters less than 7?

More Odd Numbers

The sum of a sequence of odd numbers is always divisible by half of the sum of the first and last odd numbers in the sequence. For example, 7 + 9 + 11 + 13 is divisible by ½(7 + 13), and 3 + 5 + 7 + 9 + 11 is divisible by ½(3 + 11). Why?

Odd Numbers

It's been a hectic month. I am now employed again, and have had little time for word problems. However, here's a good brain teaser.

A number is "singly even" if it can be evenly divided by 2 but not by 4. The numbers 2, 6, 10, 14, 18, ... are all "singly even." Show that the sum of a sequential series of odd numbers (e. g., 9 + 11 + 13 + 15) must be odd or divisible by 4; it cannot be "singly even."

Room Volume

A room is 15' long, 12' wide, and 8' high. What is the volume of the room in cubic feet?

Seventy-two

For each of the following three-digit numbers, insert one digit anywhere to make a number divisible by 72.

151, 352, 511, 722, 812, 993

Room Size

A rectangular room has an area of 132 square feet. The sides of the room are in whole feet. What are the most likely length and width of the room?