September 2009
Problem of the Month

Blip, Blop, Bleep Problem

Every Blip is a Blop.
Half of all Blops are Blips.
Half of all Bleeps are Blops.
There are 30 Bleeps and 20 Blips.
No Bleep is a Blip.

How many Blops are neither Blips or Bleeps?

Solution to the Problem:

There are 5 Blops that are neither Blips nor Bleeps.

The Venn diagram below shows the distribution of Blips, Blops, and Bleeps.   Since it is given that there are 30 Bleeps and 20 Blips, then there must be 40 Blops (since half of all Blops are Blips).   Since Half of all Bleeps are Blops, there are 15 Bleeps that are Blops.   Since there are 20 Blips that are Blops and 15 Bleeps that are blops, that leaves 5 Blops that are neither Blips nor Bleeps.

Correctly solved by:

1. K. Sengupta	Calcutta, India
2. Cameron Burkholder	Virginia Tech, Blacksburg, Virginia
3. David & Judy Dixon	Bennettsville, South Carolina
4. Jacob Harmon	Mountain View High School, Mountain View, Wyoming
5. Meagan Leonard	John Handley High School, Winchester, Virginia

Send any comments or questions to: David Pleacher