Friday, February 7, 2014

How does it work?

Here is a number magic trick that came to me via mail.
All of you, math detectives, are invited to unveil its magic with your logic.
  1. Take the last digit of your mobile phone number.
  2. Multiply this digit by 2.
  3. Add 5 to the result.
  4. Multiply what you got by 50.
  5. Now, you may need a calculator. Add to the previous result 1763. And if you already celebrated your birthday in 2014, add another 1.
  6. Last step! Subtract the year of your birth.
You should now have a 3-digit number.
Its first digit is the last digit of your mobile phone number and the next two digits are your age!


How does it work? Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon

8 comments:

Anonymous said...

y=the last digit of a mobile phone number
The operations that are performed on y result on in following algebraic expression:
(((y*2)+5)*50)+1763-birthyear+1(if birthdate already occurred in 2014)

Simplifying this expression yields:
100y+250+1763-birthyear+1(if birthdate already occurred)

This simplifies further to:
100y+2013-birthyear(+1,if birthdate occurred)

This expression yields a 3-digit number.
In the hundreds place is the mobile phone digit provided earlier(y).

The other two digits of the 3 digital number will be the person's age.
If the person had passed their birthday in 2014, their age is 2013+1 minus their birth year
If the person has not yet passed their birthday in 2014, their age is 2013 minus their birth year

good problem, though it ended up being easier than I initially thought it would.

Cheers,
TracyZ

dave krause said...

This is an Algebraic Proof where
‘c’ is Cell # digit
‘b’ is Birth Year
‘a’ is Age

The equation is : [2 x c + 5] x 50 + 1763 - b = 100 x c + a

Cell # digit is immaterial to the equation. The only pertinent indicators to the solve are your Age and Year of Birth.

Cell # digit falls out of the equation.

100c + 250 + 1763 – b = 100c + a
2013 – b = a
2013 = a + b

Some examples :
If ‘c’ is 4 , ‘b’ is 1995 , and ‘a’ is 18 with a date of birth occurring in December, the equation resolves to :

[2 x (4) +5] x 50 + 1763 – 1995 or
[ 13 ] x 50 – 232 which equals 418

And if we change the Birth Year to 2005 indicating an Age of 8, we have :
[2 x (4) +5] x 50 + 1763 – 2005 or
[ 13 ] x 50 – 242 which equals 408

Resulting in the 1st digit as your cell # digit and the latter two numbers, as your age


Annie said...

I started by trying to solve for the last digit in my phone number to see how the numbers were working: so, the last number in my cell phone number is x and, following the instructions, then 2x; then (2x+5); then 50(2x+5) + 1763. This equals 100x + 250 + 1763 or 100x + 2013. 2013 is an interesting number here...last year.... or for most, the last year we celebrated a birthday. And if you add 1 it would be the year of your last birthday for the others. If you subtract your year of birth, you will get your age + 100x, so since the last number in the phone number is a single digit, the number in the hundreds column would be x. I think these particular instructions would fall apart if you are 100 or more as it would add to the hundreds column or the last digit in the phone number. The age must be two digits only.

Dennis (of Dennis and Katrina) said...

Step 1. Let the last digit of your phone number be "n"
Step 2. Multiply by 2 = 2n
Step 3. Add 5 = 2n + 5
Step 4. Multiply by 50 = 50*(2n+5) = 100n + 250
Step 5. Add 1763 if you haven't had your birthday, add 1764 if you have. This will give you either:
100n + 2013 OR 100n + 2014. Those numbers should be a clue as to what's happening.
Step 6. Subtract the year of your birth. That will give you 100n + "your age", since 2013/2014- birth year will result in your current age.

Whatever the last digit of your phone is, mulitplying it by 100 simply moves the digit to the hundreds place; adding your age makes a three digit number where the first digit is the last digiit of your cell number and the next two are your age - with some caveats!

First - what happens if my cell number ends in zero? 100*(0) is zero; when I do the rest of the calculations, I only get a two-digit number... some could argue there's a leading zero there, but I don't think leading zeros are the best math.

Second, it doesn't work if you are older than 99 years old!

Dennis

Anonymous said...

It seems to me that the reason it works is because the year of my last birthday (2013) is the answer after adding 1763 except for the hundredths place. The number in the hundredths place is the number of the last digit of the phone number. I tried it using different digits. Multiplying the first answers by 50 put the last phone digit in the hundredths place. You get to the tens place by adding 5 to the 2 x last phone digit. In other words. tens place times 50 equal between 100 and 900.

Gurubandhu

Jerome said...

The key to this is in following the steps.
Last digit of the cell phone . . . . . . . . . . . . . x
Multiply by 2 . . . . . . . . . . . . . . . . . . . . . . .2x
Add 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . .2x + 5
Multiply by 50 . . . . . . . . . . . . . . . . . . . . . .(2x + 5)*50 = 100x + 250
Add 1763 . . . . . . . . . . . . . . . . . . . . . . . . .100x + 250 + 1963 = 100x + 2013
Now subtract the date of birth . . . . . . . . . . The hundred x will not be effected leaving your age.

The result is your age in the 10s and units places and the last digit of your phone's last digit in the hundreds place.

I am not considering those poor souls that have birthdays in January or in February up to the 10th.

Jerome said...

0 for my answer as the digit for the phone (our house phone ends in a zero) is not terrific because it leaves a 2 digit number. If that happens you have to know that the phone number is a zero. Also this will give grief if you are over 99 I think.

Maria said...

Very impressive! What is magic for some is just a number manipulation for others.
You are right - it works only if you are between 10 and 99 years of age. But you are, right?

Darla wrote to me via email that it is too easy.
I should say that it is only for those of us who are friendly with numbers. I received this trick via email from my mom and in the email chain underneath the forward there were a lot of surprised voices:
"Wow, it worked for me!!!"
"Me too?!!!"
"And for my age:)"
"And me!"

A puzzle point for everyone who answered.

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