Expert: Scott A Wilson - 10/23/2008

Question
Hi Scott,

Please let me know if u know the trick to make quick calculations. Like, for example 333 times 131.. Is there any trick with this?

Thanks in advance

Answer
For that specific example, yes.  Divide 131 by 3 and you get 43 2/3.
So the answer is 43,666 - 43 = 43,623.  That's only because 3*333=999.

Other tricks are to know that *5 is the same as *10/2.
If you take 1673*5, it's ....
but if you know it's the same as 1673*10/2, it can be seen to be 8,365.

Note that I have several rules to see if the math was done right that I could send to you for several numbers.  Besides 2,3,5 and 9, they start getting a little bit tricky, but easier than multiplying the numbers together.  For 11, take the sum of the odd digits minus the even digits.  If you get a number divisible by 11, the

For squares, not the 17²=289.  67²=(50+17)²=50²+1700+17²=4,489.
117²=100²+2*1700+289=13,689.  217²=200²+4*1700+289=47,089.  That was kind of cool.  But I can do the same thing with minus signs.
83²=(100-17)²= 10,000-2*1,700+289=6,889.  
483²=500²-17,000+289=233,289.  Those are just a small number of facts I did with 17.  What's really freaky is when I get the answer, I think, yeah, that's right.

Know the first 25 squares, and you can do almost anything since 26²=24²+100, 27²=23²+200, (25+a)²=(25-a)²+a*100.

Now late at night, when I'm going to sleep, I take the days date.  I notice today is the 23rd.  23*23=529.  529*23=12,167.  12,167*23=279,841.  279.841*23= (I have to think now) 6,436,343.  Not the weird occurences of 43 and 6.  Also note that I recognize 343 as 7^4 or the 343=2,401/7 and 2,401²=5,764,801.  That's about enough with 23.  On to 33=3*11.  

2: 3*3=9, 3*11=33, 11*11=121.   
3: 3*3*3=27, 3*3*11=99, 3*11*11=363, 11*11*11=1,331.  
4: 3*3*3*3=81, 3*3*3*11=297, 3*3*11*11=1,089, 3*11*11*11=3,993, 11*11*11*11=14,641.
I keep going, adding one more digit until I get up to 7 or more.
7:3*3*3*3*3*3*3=2,187, 3*3*3*3*3*3*11=729*11=8,019, 3*3*3*3*3*11*11=243*121=29,403, 3*3*3*3*11*11*11=81*1,331=106,480+1,331=107,811, 3*3*3*11*11*11*11=27*14,641=292,820+102,487=395,307,
3*3*11*11*11*11*11=9*161,051=1,449,459.
3*11*11*11*11*11*11=3*1,771,561=5,314,683.
11*11*11*11*11*11*11=19,487,171.
I had to stop and think for a few seconds to get the ones with three or four 3's, but the rest I know.
I even know 11^8 is 214,358,881 and I recognize the prime factors of 214 as 2*107, 358 is 2*179 and 881 is prime (I believe - just a moment - yes, it is - only have to check 2,3,5,7,1,13,15,17,19,23, and 29).

Now 43 is prime and the square is 50²-700+7²=1,849.  1,849*43=73,960+5,547=79,507. 79,507 (yes, I recognize once I get it) * 43=(80000-500)43+ 7*43=4,418,500+301=3,418,801 (I had to make sure in Excel, but it's right).

I keep going with 53 (prime), 63 (3*3*7), 73 (prime), 83 (prime), 93 (3*31), 103 ... now that's an interesting one.  103^2=10,609.  Note that 1²=1, 2*3=6, and 3²=9.  Ever seen that special triangle where each row is the sum above it?  It goes 1, 1 1, 1 2 1, 1 3 3 1, 1 4 6 4 1, 1 5 10 10 5 1, 1 6 15 20 15 6 1, 1 7 21 35 35 21 7 1, ...
you know 10 is 4+6 or 6+4, 15 is 5+10 and 10+5, 21is 6+15 and 15+6 ... oh yeah - that's called Pascal's triangle.  I've even done strange things with that, like make one side counting (1,2,3...) and left the other side 1's.
Now back to the powers of 103.  103 to the 5 is then 10,000,000,000+300,000,000+9,000,000+270,000+8,100+243 since the powers of 3 are 3, 9, 27, 81, and 243.  That's 10,309,278,343.   Hey, did you know that 343 is 7^3?  In fact, 10=2*5, 309=3*103, 278=2*139, and 343=7*7*7 (prime factors).

It all comes down to one thing - numbers are my thing.  I do them a lot and sometimes take a break to eat or talk to someone else.  I don't know if I do them in my sleep yet, but while I'm going to sleep, I just take that day's date and have fun (as I already told you).  It's fun to me, anyway.

I also play songs on the piano by ear a lot.  There are hundreds of songs that if I remember the song, I can play it in the key of C.  I'm getting so I can easily shift to the key of D, F, and G.  On some songs, I've shifted them to almost every normal key (there are twelve of them).  I haven't yet shifted a song to a minor key or a diminished key, though.  I've played hundreds of songs for over half a dozen different churches.

Basically, you hit my hot spot - the spot where I know a lot and then some more.  I'm sure I could tell you ten times this much without a problem, but I don't think I should.

One last note.  (a-b)(a+b)=a²-b², so if the difference between two numbers is an even number, you can find a=(n1+n2)/2 and b=(n1-n2)/2.  This shows that the squares are all you need to know.  Of course, if the difference is odd, use a-1 and then add b into your final answer.  As it says in the million dollar question on TV (seen that?), that is my final answer.