# Another math trick

#### Mark44

Joined Nov 26, 2007
628
This one requires a willing participant with a calculator...

1. Ask the willing participant to think of a three-digit number, and to commit it to memory or write it down so that you can't see it.
2. Ask your friend to key in the digits of the number, and then key them in again, forming a six-digit number. For example, if the first number was 283, the number keyed in should be 283283.
3. Ask your friend to divide the number in the previous step by 13. Surprisingly, the result is an integer.
4. Now ask your friend to divide the number in the previous step by 11. Again, the result is an integer.
5. Finally, ask your friend to divide the number in the previous step by 7.
6. Tell your friend that this is the same number he/she started with.

Can someone come up with an explanation of how this works?

#### Dave

Joined Nov 17, 2003
6,970
Fantastic! I really like this one!

If someone hasn't already solved this by tomorrow I will sit down and have a go at working it out. We have friends round later so might crack the calculator out along side a bottle of wine!

Dave

#### Dave

Joined Nov 17, 2003
6,970
Got it with a bit of algebra!!

I won't ruin it for others though...

Dave

#### hgmjr

Joined Jan 28, 2005
9,029
Got it with a bit of algebra!!

I won't ruin it for others though...

Dave
Dave,

I too have detemined the underpinning algebra that makes this work. It was fairly transparent.

hgmjr

#### thingmaker3

Joined May 16, 2005
5,084
The answer becomes obvious when one simplifies the division.

#### mrmeval

Joined Jun 30, 2006
833
Try two digits but divide by 101.

#### hgmjr

Joined Jan 28, 2005
9,029
Or try 4 digits and divide by 10001.

Example number: 12341234

The result would be 1234

hgmjr

#### Mark44

Joined Nov 26, 2007
628
Or try 4 digits and divide by 10001.
Yes, that will work, but will seem more transparent to the trickee. Part of the mystery of the original version is the apparent disconnect between the 1001 multiplier and its factors--7, 11, and 13.

#### Dave

Joined Nov 17, 2003
6,970
I tried this trick on my missus and she wasn't impressed, so I then tried to explain it and she became even less impressed!

It must be bloke thing!

Dave

#### Mark44

Joined Nov 26, 2007
628
My wife is like that, too. She's definitely a "people" person, and has zero curiosity about "math" things, a category into which she lumps chemistry, physics, biology, computer programming, and of course math (or maths, as you would say).

Her lack of appreciation in this area is partly due, I think, to her experience in high school geometry. The teacher was a very uninspiring guy with no sense of humor and a generally sour demeanor. After an experience like that, a lot of people just give up, and in essence wall off large sections of human thought.

#### Dave

Joined Nov 17, 2003
6,970
My wife is like that, too. She's definitely a "people" person, and has zero curiosity about "math" things, a category into which she lumps chemistry, physics, biology, computer programming, and of course math (or maths, as you would say).
It is a curiosity why we consider it a plural (Maths) you guys consider it a singular (Math)!! Funilly enough if we call it "Math" over hear it just sounds wrong. My web browser spell-checker pulls up Math but not Maths!

Her lack of appreciation in this area is partly due, I think, to her experience in high school geometry. The teacher was a very uninspiring guy with no sense of humor and a generally sour demeanor. After an experience like that, a lot of people just give up, and in essence wall off large sections of human thought.
Yes, its a common issue for such an important subject. My missus wasn't taught by a bad teacher, and she really liked Maths, but as a nurse she feels there is probably more to like than the geekery that we crave so much here.

Oh well!

Dave

#### 240Volts

Joined Apr 30, 2008
1
wow thats a cool trick

#### wiltec

Joined May 12, 2008
3
YOUR NUMBER CAN BE REPESENTED BY xyzxyz WHICH REALLY IS : 100000x + 10000y + 1000z +100x + 10y + z, which is: 100100x + 10010y + 1001z, which is:
1001 x (100x + 10y + z). 1001 = 13 x 11 x 7 and 100x + 10y + z is really the number xyz.

#### triggernum5

Joined May 4, 2008
216
What factors would be good to make it work with 8008, 80085, or 80084, or even 8008135? I love a good math trick that works with those..

#### K8MHZ

Joined Jun 1, 2008
6
Here is a fun one for all of you!

This is my first post here. I hope you like it. This seems to be a great forum. I am also a senior member of Mike Holt's Forum and a long time member of QRZ. Forums are great ways to learn and network.

Cheers and 73

Mark aka Marky the Sparky

#### thingmaker3

Joined May 16, 2005
5,084
Welcome to AAC, Marky!

The first part of the "mind-reading trick" in this is a limited number of numbers. IE f(11)=9, but f(13) also = 9. The solution for f(x) where x is a 2 digit number are limited to 9, 18, 27, 36, 45, 54, 63, 72, and 81. Specifically, f(x) = 9 * INT(x/10)

Second part of the trick is to assign a random zodiacal sign to the numbers. Same sign gets assigned to all multiples of 9. Other signs get put on non-solution numbers.

#### K8MHZ

Joined Jun 1, 2008
6
Welcome to AAC, Marky!

The first part of the "mind-reading trick" in this is a limited number of numbers. IE f(11)=9, but f(13) also = 9. The solution for f(x) where x is a 2 digit number are limited to 9, 18, 27, 36, 45, 54, 63, 72, and 81. Specifically, f(x) = 9 * INT(x/10)

Second part of the trick is to assign a random zodiacal sign to the numbers. Same sign gets assigned to all multiples of 9. Other signs get put on non-solution numbers.
Thanks for the welcome!

Yep, you got it! It's still a cool trick for the masses. My sister sent it to me and was totally freaked out by it.

As for astrology, I used to put astrology and weather forecasting into the same group....until I realized that astrology has some basis in scientific fact. (I live near Lake Michigan, the hardest place to forecast the weather in the country)

Again, thanks for the welcome. This seems like a great forum!

#### circuitashes

Joined May 13, 2008
37
YOUR NUMBER CAN BE REPESENTED BY xyzxyz WHICH REALLY IS : 100000x + 10000y + 1000z +100x + 10y + z, which is: 100100x + 10010y + 1001z, which is:
1001 x (100x + 10y + z). 1001 = 13 x 11 x 7 and 100x + 10y + z is really the number xyz.
I realised this also. Great work. This explains why the ff are true:
(1001*(100x + 10y + z))/13 = (100x + 10y + z)*11*7 = an integer
((1001*(100x + 10y + z))/13)/11 = (100x + 10y + z)*7 = an integer
(((1001*(100x + 10y + z))/13)/11)/7 = 100x + 10y + z = xyz,
for all x,y,z

This completely explains the trick.

#### ahrjay007

Joined Jul 9, 2008
3
i lyk that trick...awesome

#### DrMarten

Joined Aug 11, 2008
5
This one requires a willing participant with a calculator...

1. Ask the willing participant to think of a three-digit number, and to commit it to memory or write it down so that you can't see it.
2. Ask your friend to key in the digits of the number, and then key them in again, forming a six-digit number. For example, if the first number was 283, the number keyed in should be 283283.
3. Ask your friend to divide the number in the previous step by 13. Surprisingly, the result is an integer.
4. Now ask your friend to divide the number in the previous step by 11. Again, the result is an integer.
5. Finally, ask your friend to divide the number in the previous step by 7.
6. Tell your friend that this is the same number he/she started with.

Can someone come up with an explanation of how this works?

Hi,

I will have to check this with a computer program in Visual Basic.Net ( VB.Net )

It seems that as 13 times 11 times 7 is 1001

so maybe all numbers of the form XYZXYZ like 123123 are divisible by 1001

If that is TRUE that is the reason it works.

I'm off to test it now!!

Regards,

DrM.