Find two factors (other than 1 and the number itself) whose product is:
612 + 88 + 278
Set 16
Sum of Odd #s is the Squares 2
What is the sum of the first n odd numbers? (The first five odd numbers are 1, 3, 5, 7, 9.)
Squares & Cubes Pattern
Examine the numerical statements in the box. Something is going on.
What would the statement be for 1003?
What would the statement be for n3?
Can you prove that it always works?
Factorials as Perfect Squares
The first few factorials greater than 1 are clearly not perfect squares: 2! = 2, 3! = 6, 4! = 24, etc.
Question: Can n! be a perfect square for some n > 1? Decide and give your evidence.
Consecutive Numberss All 1’s and 2’s
The smaller of two consecutive natural numbers is divisible by 23 and the larger by 29. Find the smallest pair of such numbers with the property that they both contain only the digits 1 and 2.
Spare Tire, Alaska
Ed traveled 5000 miles round-trip between home and Fairbanks in a car with one spare tire. He rotated tires at intervals so that when the trip ended, each tire had been used for the same number of miles. For how many miles was each tire used?
Large Multiples of 17
What is the largest multiple of 17 that can be diplayed on an 8-digit calculator?
Pattern to Formula
Find as many numbers as you can that have the pattern shown here:
52 – 5 = 42 + 4
72 – 7 = 62 + 6
72 – 7 = 62 + 6
Pretty easy, eh? Write a formula to see why.
Balloon Club Committees
In the Hot Air Balloon Club each member is on two committees, and any two committees have exactly one member in common. There are five committees altogether. How many members does the club have?
Chain Links
Here are 5 lengths of chain, 3 links each. It costs 5 cents to break a link open, and 10 cents to weld a link closed again. How much will it cost to weld these pieces together into one length of chain with 15 links in it? (Less than 60 cents!) Explain how to do it.