Moving Along Down the Football Field 

One fine fall day, Fred the football player decided to do a little math activity with his favourite sport, so he put his ball down on one of the goal lines of the 100-metre field. He then moved it forward half the distance - that is, 50 metres - toward the other goal line. Next he moved it half the remaining distance, 25 more metres.

He planned to continue in this manner as long as he could, always advancing the ball half the remaining distance toward the other end. Of course, it should be obvious that sooner or later his moves would be quite small.

The question is: on which move of the ball would the distance first become less than one centimetre?

Bonus: What would be the total distance that Fred moved the ball after that move? Give your answer rounded to the nearest 100th of an centimetre.

Comments

 This problem (with some solutions) is based on one found at : http://mathforum.org/midpow/solutions/solution.ehtml?puzzle=47

email me                          Thursday, 11 July 2002