June 25, 2012

Geometry: Triangle A has sides
5, 5, and 8, and triangle B has sides 5, 5, and 6. What is the ratio of
the areas of the two triangles, A/B?

From NCTM

Answer available July 2, next puzzle

Answer to math puzzle of June 18

Number theory: Exactly 2 integers less than 100 have exactly 5 different factors. What are they, and what are the next 2 such integers LARGER than 100?

From JLS Middle School May-June Einsteins

Solution: normally composite numbers have an even number of factors. The exceptions are all squares. The simplest is 16 with 1,2,4,8,16. All the rest are odd. In fact all the numbers with exactly 5 factors are 4th powers of prime numbers: 3^{4} = 81 (also less than 100), and 5^{4} = 625 and 7^{4} = 2401

©copyright 2012, Louis
Bookbinder - booky1@earthlink.net

updated 25 June 2012

From NCTM

Answer available July 2, next puzzle

Answer to math puzzle of June 18

Number theory: Exactly 2 integers less than 100 have exactly 5 different factors. What are they, and what are the next 2 such integers LARGER than 100?

From JLS Middle School May-June Einsteins

Solution: normally composite numbers have an even number of factors. The exceptions are all squares. The simplest is 16 with 1,2,4,8,16. All the rest are odd. In fact all the numbers with exactly 5 factors are 4th powers of prime numbers: 3

updated 25 June 2012