UCD Openday 2000
Mathematics Problem
You must follow the rules.
Can you light up all the bulbs?
Sixteen light bulbs are arranged in a square grid,
as shown. There is a switch for each row and for each column.
Flicking a switch turns any unlit bulb on and any lit
bulb off, but only in the associated row or column.
-
Can all sixteen bulbs be turned on,
starting with the configuration of six lighted bulbs shown above?
-
What is the greatest number of bulbs that can be turned off
at the same time,
starting with the configuration of six lighted bulbs shown above?
-
The electrician chooses a starting configuration to save electricity.
Using optimal switching a computer then turns on the maximum possible
number of bulbs. The electrician gets a pound for
every bulb which remains unlit.
What is the most the clever electrician can earn?
UCD Openday 2000 Mathematics Problem
Page maintained by
jbquig@ucd.ie
Revised 17 Mar 2000.