March 18, 2013

Geometry: In April 2012 I put up a puzzle asking to dissect a regular
hexagon into 8 congruent quadralaterals. I showed a solution but now I
found
another solution. What is it?

From NCTM

Answer available March 25, next puzzle

Answer to math puzzle of March 11

Algebra: The harmonic mean of two integers a and b is defined as 2ab/(a+b). If the larger integer is twice the smaller and the harmonic mean is 1 less than the arithmetic mean ((a+b)/2) what are the numbers?

From NCTM

Solution: If b is twice a then the harmonic mean is 4a^{2}/ 3a or 4a/3. The arithmetic mean is 3a/2 so 3a/2 = 4a/3 + 1. So, a = 6 and b = 12.

©copyright 2013, Louis Bookbinder - booky1@earthlink.net

updated 18 March 2013

From NCTM

Answer available March 25, next puzzle

Answer to math puzzle of March 11

Algebra: The harmonic mean of two integers a and b is defined as 2ab/(a+b). If the larger integer is twice the smaller and the harmonic mean is 1 less than the arithmetic mean ((a+b)/2) what are the numbers?

From NCTM

Solution: If b is twice a then the harmonic mean is 4a

updated 18 March 2013