**Here's a look at the questions:**1. A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost? 2. If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets? 3. In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? These are the three most common answers that people guess - but they are actually

**incorrect.**1. 10 cents 2. 100 minutes 3. 24 days Professor Frederick adds: "Anyone who reflects upon it for even a moment would recognise that the difference between $1 and 10 cents is only 90 cents, not $1 as the problem stipulates. "In this case, catching that error is tantamount to solving the problem, since nearly everyone who does not respond '10 cents' does, in fact give the correct response."

**The correct answers are:**1. 5 cents 2. 5 minutes 3. 47 days Still puzzled by all of this? Thankfully, Presh Talwalkar, the author of The Hoy of Game Theory: An Introduction to Strategic Thinking explained how to work out the correct answers on his blog, Mind Your Decisions. 1. Say the ball costs X. Then the bat costs $1 more, so it is X + 1. So we have bat + ball = X + (X + 1) = 1.1 because together they cost $1.10. This means 2X + 1 = 1.1, then 2X = 0.1, so X = 0.05. This means the ball costs 5 cents and the bat costs $1.05 2. If it takes 5 machines 5 minutes to make 5 widgets, then it takes 1 machine 5 minutes to make 1 widget (each machine is making a widget in 5 minutes). If we have 100 machines working together, then each can make a widget in 5 minutes. So there will be 100 widgets in 5 minutes. 3. Every day FORWARD the patch doubles in size. So every day BACKWARDS means the patch halves in size. So on day 47 the lake is half full.