Last week I played “Bridge over Troubled Water” for my students and described Paul Simon, the composer, as a genius. Yesterday I read a story about Carl Gauss, another genius, known for his contributions to mathematics. When Carl was in primary school his teacher gave him a task to keep him busy: Determine the sum of all the whole numbers 1 thru 100. The teacher imagined that Carl would use pencil and paper to add the numbers: 1+2+3… Instead, Carl looked at the teacher for a moment and gave him the answer. Can you determine the answer without any external help, even from pencil and paper? I couldn’t. I will put the answer below.
Was Charles Dickens a genius in writing novels? He saw extreme poverty and wrote about it with the goal of changing government policy, which had been very harsh toward the poor. After he published “Ä Christmas Carol”,” the government changed its policies, and the world had a story for the ages.
Other individuals are extremely talented in athletics, in organizing others, in helping others, in making others laugh, in parenting, etc. Howard Gardner of Harvard University invented the term “multiple intelligences” to describe ability in different realms of life.
Are you a genius in some aspect of life? If not, what would it take to move into the genius range? More effort, more learning, more experience?
For me as a scientist, I try to think of new ideas — novel ideas with power in them. What about you — which of your goals give you the opportunity to show genius?
The correct answer to the Gauss question is 5,050. My answer was 5,000, but I had a feeling I might be wrong. Here is one way to answer the problem in your head: Divide the 100 numbers into 1-50 and 51-100. The median is 50.5 (half way between 50 and 51). Assume that in a set of consecutive whole numbers, the median always equals the mean. Take the mean, 50.5, and multiply that times the number of numbers (100) to determine the total of the numbers. You can do that by moving the decimal two places to the right. Then 50.5 becomes 5050.0
John Malouff, PhD, JD
Assoc Prof of Psychology
I thought it said 1000 and thus got to 500500 … by thinking 1000 + (999 + 1) = 2000 therefore the pattern must continue + 500
Hi KB. It is a hard problem — an unusual one. I just read how Gauss solved the problem. In his head he lined the numbers up 1,2.3, etc., lined up the numbers in a row below in reverse order, 100, 99, 98, noted that each upper and lower pair added to 101, multiplied that by 100 (there were 100 numbers) and divided by 2 (he used two sets of numbers). That gave 10100/2=5050. He then developed a formula following this pattern that one can use for solving such problems. For more info, Google: Gauss series.
Hi John,
I often use the question ‘what are you famous for?’ as an icebreaker when I’m training small groups. I get some great answers but sometimes I need to prompt by telling them ‘I’m famous for driving an old landrover and having adventures’. It can be a great insight into peoples view of themselves.
I might start asking ‘what are you a genius of (or in)?’ and see what sort of answers that generates! I like the idea of chosing an area that you might almost be a genius and then working towards that goal.
Thanks for this blog, BTW, long-time-reader, first-time-poster…
Cheers,
Adam
Hi Adam. The “genius”question sounds like a good, positive way to start a group session. I provide supervision to Lifeline volunteers, and I might now start a session with that question.