The world’s shortest IQ test has just three questions, yet fewer than one in five people can answer all three correctly. The world’s shortest IQ test is proving to be quite tough, with only 17 percent of respondents answering correctly. But how hard can it be when there are only three questions?
Dubbed the Cognitive Reflection Test, it comes from a 2005 paper by MIT professor Shane Frederick, who sought to demonstrate the difference between fast thought processes that occur with little conscious deliberation, and those that are slower and more reflective.The test consists of three brain teaser-type questions that are harder than they first appear, where the immediately obvious “right” answer is actually incorrect – if you stop and think about it.
Here are 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?
What most people guess:
1. 10 cents
2. 100 minutes
3. 24 days
As Prof Frederick noted, the intuitive answer to the first question is 10 cents, but this “impulsive” answer is wrong.
“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,” he wrote.
“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.”
Here are the correct answers:
1. 5 cents
2. 5 minutes
3. 47 days
Presh Talwalkar, author of The Joy of Game Theory: An Introduction to Strategic Thinking and an expert on mathematical puzzles, explains further 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 five cents and the bat costs $1.05.”
2. “If it takes five machines five minutes to make five widgets, then it takes one machine five minutes to make one widget (each machine is making a widget in five minutes). If we have 100 machines working together, then each can make a widget in five minutes. So there will be 100 widgets in five 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.”
In all honesty, I got the second two correct, and the first one wrong. It probably helped that I knew before taking the test that the obvious answer wasn’t correct. We are so quick to answer, even if wrong we want to hit the buzzer! I blame Alex Trebek, who is having his 79th birthday today.
Susan Saunders 7/22/19