It's clear from the "Thinking Out Loud" section that he uses the formula for the square of a sum of two numbers:
(A + B)**2 = A**2 + B**2 + 2(AxB)
I learned a trick years ago to get the square of any number ending with a 5. You multiply the rest of the number by that number plus 1 and stick a 25 on the end. For example, to square 25, you multiple 2 times 3 and stick a 25 on the end: 625. 225 squared: 22x23 = 506, so 50,625
The reason this works is because a number written "X5" is actually 10X + 5. (10X + 5)**2 = 100X**2 + 25 + 2(10Xx5)
=100(X)(X + 1) + 25
When he squared the five-digit number, he was doing something similar: "AB,CDE" = 1000("AB") + "CDE", so
"AB,CDE"**2 = 1,000,000("AB")**2 + 2(1000"AB")("CDE") + "CDE"**2. He used some sort of verbal code to store the intermediate sums.
Of course, that just explains how he does it. That doesn't mean it's EASY!
I know the problem I always had (I don't do that much estimating anymore, so I've fallen out of the habit of doing mental calculations that much) was how to remember the intermediate numbers that you would eventually add up for the result.
The words must make storing those preliminary results easier to retain, but, to the uninitiated, it seems to only make it more complicated...
The calendar thingy still freaks me out though. That's where I think an innate ability comes more into play, though it would be interesting to "see" the process there as well...
Of course, there are "only" fourteen different calendars (one beginning each day of the week, either leap year or not). There is probably a relatively simple way to know which calendar it is from the last three digits of the year. Then, you could memorize the number of days preceding the month in question (e.g., 0 for Jan., 31 for Feb,. 59 or 60 for Mar,. 90 or 91 for Apr., etc.). The date then is added to the total. Divide by seven and take the remainder. So, Apr. 15, 1991 is the 105th day of the year (not a leap year). Divide 105 by 7, giving 15 with no remainder. The day of the week, then, is the same as the seventh day of 1991. If you knew that 1991 began on a Tuesday, you would then know that Apr. 15 was a Monday.
Recommended Posts
shazdancer
Whoa, I are impressed! Thanks for the link, George.
Link to comment
Share on other sites
George Aar
Gee, I thought I was hotstuff when I could mulitply 3-digit numbers in my head!
I wonder though, how much of what he does could actually be done by most anyone, with enough practice, and how much is simply an innate ability?
Nature or nurture, either way he's an amazing performer...
Link to comment
Share on other sites
GeorgeStGeorge
It's clear from the "Thinking Out Loud" section that he uses the formula for the square of a sum of two numbers:
(A + B)**2 = A**2 + B**2 + 2(AxB)
I learned a trick years ago to get the square of any number ending with a 5. You multiply the rest of the number by that number plus 1 and stick a 25 on the end. For example, to square 25, you multiple 2 times 3 and stick a 25 on the end: 625. 225 squared: 22x23 = 506, so 50,625
The reason this works is because a number written "X5" is actually 10X + 5. (10X + 5)**2 = 100X**2 + 25 + 2(10Xx5)
=100(X)(X + 1) + 25
When he squared the five-digit number, he was doing something similar: "AB,CDE" = 1000("AB") + "CDE", so
"AB,CDE"**2 = 1,000,000("AB")**2 + 2(1000"AB")("CDE") + "CDE"**2. He used some sort of verbal code to store the intermediate sums.
Of course, that just explains how he does it. That doesn't mean it's EASY!
George
Edited by GeorgeStGeorgeLink to comment
Share on other sites
George Aar
Yeah, the verbal code was interesting.
I know the problem I always had (I don't do that much estimating anymore, so I've fallen out of the habit of doing mental calculations that much) was how to remember the intermediate numbers that you would eventually add up for the result.
The words must make storing those preliminary results easier to retain, but, to the uninitiated, it seems to only make it more complicated...
The calendar thingy still freaks me out though. That's where I think an innate ability comes more into play, though it would be interesting to "see" the process there as well...
Link to comment
Share on other sites
GeorgeStGeorge
Of course, there are "only" fourteen different calendars (one beginning each day of the week, either leap year or not). There is probably a relatively simple way to know which calendar it is from the last three digits of the year. Then, you could memorize the number of days preceding the month in question (e.g., 0 for Jan., 31 for Feb,. 59 or 60 for Mar,. 90 or 91 for Apr., etc.). The date then is added to the total. Divide by seven and take the remainder. So, Apr. 15, 1991 is the 105th day of the year (not a leap year). Divide 105 by 7, giving 15 with no remainder. The day of the week, then, is the same as the seventh day of 1991. If you knew that 1991 began on a Tuesday, you would then know that Apr. 15 was a Monday.
Straightforward, but again, not easy.
George
Link to comment
Share on other sites
waysider
Here's a way to do the birthday thing:
----------------------------
Year + Year/4(ignore decimal) + Day + SV
______________________
-----------7-----------
SV Table(Significant Value)
-----------
Jan=0-------------July =6
Feb=3-------------August=2
March=3----------Sept.=5
April=6-----------Oct.=0
May=1------------Nov.=3
June=4-----------Dec.=5
So----- here's an example: 10/11/1940(use only the last two digits of the year)
40+10(because that is 40/4)+ 11 + 0
__________________________________ =8 with a remainder of 5
---------------7--------------------------------
The remainder tells you the day of the week, using this chart:
0=Sun.
1=Mon.
2=Tues.
3=Wed.
4=Thurs.
5=Fri.
6=Sat.
Thus, 10/11/1940 was a Friday.
Note
Dividing by 4 adjusts for leap year.
Dividing by 7 adjusts for the number of days in a week
--------------------------------------------------------------------------------------------------------------
That little trick is in one of the "Human Calculator" lessons that Scott Flansburg did a few years ago
Link to comment
Share on other sites
J0nny Ling0
Well, I can play the harmonica rather well...
Link to comment
Share on other sites
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.