I recently started reading “Don’t you have time to think” by who else? Richard Feynman. It is a collection of letters written by him and to him.
In November 1939 Feynman wrote a letter to his mother with a puzzle attached (for his father). See the image.
I challenge everyone to find the solution to this puzzle – without using a calculating device. It took me about 4 hours – a wonderful exercise in logical arithmetic. (REMEMBER!! NO CALCULATOR!!)
Is it just me, or were people smarter in 1939? Feynman’s father was a uniform salesman and Feynman expected him to be able to solve this. Salespeople (the middle class) in those days had to do pencil and paper arithmetic – There were no calculators.
Did the invention of the pocket calculator make us lazy? Or did it free our time to do more worthwhile things. In my opinion, it made large portions of the population EXTREMELY lazy, while the infinitesimal rest went on to do more worthwhile things – which ironically includes mental arithmetic methinks.
Today people just hear the words “Mathematics” or “Physics” and they say “Oh, your one of the smart people…” when in fact I am not that smart, they are just lazy… comment?
I can certainly see in the kids that I teach, that they find it hard to follow an algorithm that stretches for more than 5 lines… I will definitely ask them what “long division” is, and I bet more than half will go “huh?” Will maybe post a follow up.
A new year’s resolution of mine was to improve my mental arithmetic. I was never forced to learn my times table! So I never did… I was one of those reaching for the calculator when confronted with 48 divided by 8!! I have improved a lot, for one I know my times table better… Not perfect but much better. I must say it has become a fun exercise! Trying to go as far as possible doing long division in my head while driving – working out exactly how much I paid for parking per hour etcetera.
Another challenge to my brothers and me (or anyone with programming experience): Not a question of if, but of who can find the time first, to write a little (Python) script generating Feynman long division puzzles.
- 50% for a script generating puzzles with solutions (existence).
- 75% for a script generating puzzles with unique solutions (uniqueness).
- 100% for a script categorizing the difficulty of the generated puzzle (with a unique solution).
10 comments:
How fast the world is changing, that even our schooling differs a lot. I have vivid recollections of being drilled on multiple tables with corporal punishment.
One teacher made everybody in the class stand up and asked each one a multiplication sum. If you had it wrong you got a smack and kept standing for another round. If you had it right you could sit down.
The headmaster had a habit of making you a "Corporal", i.e. two lines (on your but) if you dare get less than 16/20 for his weekly test.
Not sure if the various forms of physical and metal battering was worth the fact that I could give the answer to 48 divided by 8 in an instant?
spoiler follows below (took me hours!)
a=8
484
7289
3527876
my, this is ablolutely brilliant. And damn, it is difficult! do u have any other feynman brainteasing problems?
I taught physics and chemistry before retirement - plus all of the other things you are asked to teach in a private boarding school. Always loved Feynman. A lot of the physics and math passed over my head but his spirit fascinated me. I tutor online (tutor.com) and got a question about a Feynman diagram the other day. And answered it. It was followed by a question about Kant and science. Half answered that one. Great website and entry.
"Your" not one of the "smart people" if you think that's the correct way to express that point.
This puzzle isn't that hard, unless you change the rules to do it in your head.
Take a look at the first multiply,
. x .a. = ..aa Just going through the possible values of a and checking gives you 4 possible answers,
3x48=144 8x43=344 7x84=588 and 9x37=333
then you have . x .a. =..a, so you need another digit that will multiply and end with a, which will out 8x43 and 9x37 leaving either 3x48 or 7x84.
then a x .a. = .a..
if it is 4 x.48 you have (4k+1)92
which can never give you a 4
so no you know it is 7x84
This is a brilliant puzzle and if you have any similiar puzzle or knows where to find some more I would greatly appreciate it. The rule which stipulated that calculators are not allowed is not a problem to me: I was forced to learn up to the 13th times table starting from kindergarden and my Dad would cane me in the car if I recite any of it incorrectly. By the time I was in 2nd grade the entire thing was burned into my memory. Suffice to say I find this type of puzzle challenging and much more interesting than Sudoku.
By the way, you said you teach maths? I wish I had even one challenging teacher like you in elementary and high school who actually wants to impart knowledge to their students. You said, and I quote, "Is it just me, or were people smarter in 1939?". My answer is people are just as smart now as they were then: But some teachers' method of teaching Maths leaves a lot of room for improvement. My elementary and high school Math teachers taught Math as if they were teaching History or Geography: Put the questions on the board, put the answers on the board. When the bell rings they ran out of the classroom quickly. As a result only the very intelligent or hardworking students excelled.
the solution is
484
7289
3527876
A=8
it takes not more than 1:45 min to solve it without calculator if u r good at calculation
approach is as follows
(xAy) * A =(pAqrs) A>1 get solution by puttin A=2 to 9
then Think about
(xAy)* z = fgAA
Took me about 1.5 hours. I first noticed that A-A=0. Then I noticed that .*.A.= 3 digits number (key)..A. Continued the same way of thinking.
It took me about 25 minutes to solve.The book is awesome!
The ans. is 484.
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