october 26, 2010

Problem of the Week

for Tuesday, October 26, 2010

Charlie the Chimp has devised his own way of counting with his fingers. He starts with the fingers of his right hand, raising them one by one. When he puts up the fifth finger on his right hand, he puts them all back down again and raises one finger on his left hand to record that he has gone through all the fingers on his right hand once. He then continues counting, lifting the fingers of his right hand one by one but keeping the single finger on his left hand up. For example, when Charlie has counted twenty-three objects, he would have raised 4 fingers on his left hand (having gone through his right hand's fingers four times) and 3 fingers on his right hand:

One day, while he is counting the fleas on his feet, Charlie catches a glimpse of his reflection in the lake. We know, of course, that the image of Charlie is reversed, but Charlie doesn't. He confuses his right hand for his left and therefore reads his fingers wrong. If Charlie thinks that he has counted sixteen more fleas than he has really counted, how many fingers are raised on each of his hands?

Winners of the Chimp challenge