crazy phone trick, how does it work?

Question

[Grab a calculator - you won't be able to do this one in your head…]

1. Key in the first three digits of your 7-digit phone number (NOT the area code);

2. Multiply by 80;

3. Add 1;

4. Multiply by 250;

5. Add the last 4 digits of your phone number;

6. Add the last 4 digits of your phone number again;

7. Subtract 250;

8. Divide number by 2.

Did you get your phone number?

How does this work???

Answer 1

Assume my number is
first three digits = x
last four digits = y

1.
x

2.
80x

3.
80x + 1

4.
250[80x + 1]
= 20000x + 250

5.
20000x + 250 + y

6.
20000x + 250 + y + y
= 20000x + 250 + 2y

7.
20000x + 250 + 2y - 250
= 20000x + 2y

8.
(20000x + 2y) / 2
= 10000x + y

Look at it this way...
if my first three digits (x) were 123
and my last four digits (y) were 4567

Plug those into the equation I got in #8:
10000x + y
= 10000(123) + 4567
= 1230000 + 4567
= 1234567

So basically, it's taking the first three digits, multiplying that by 10,000 (which makes your final answer a 7 digit number), and adding the last four digits to it.

It's pretty clear when you work it out as an equation.

Answer 2

Cool trick its just algebra.
Imagine any phone number:
1234567 where there are 7 digits represented by different values
now here is the function described above:

((((123 * 80) + 1)*250)+4567+4567-250)/2 = 1234567
now we can see how this works by reverse algebra
multiply both sides by 2:
(((123 * 80) + 1)*250)+4567+4567-250 = 2*(1234567)
add the numbers on the ends:
(((123 * 80) + 1)*250) = (2*(1234567))-4567-4567+250
ok before we continue lets take a quick look at the right hand side, it shows that we multiply the full number by 2 and subtract the last 4 digits twice so what this does is makes the number 2*1230000, cool right?
So now look at the left side, lets distribute the 250:
(123*80)*250 + 250
now if you notice both 250 are on each side of the equation, this is ridiculous waste so we can remove both by subtraction, follow so far?
(123*80)*250 = 2*1230000 is the new simplified equation
80*250 is equal to 2000 so lets write the equation again:
123*2000 = 2*1230000
lets now divide each side by 2:
123*1000 = 1230000 cool right?
both sides were equal all along we just proved it now,
there are infinite ways you can make this happen, this just happens to be one of them. Also note if we switched the numbers 1234567 with anything the algebra checks because everything is independent of the variable(phone number), so as long as it is 7 digits long it checks.
Enjoy!

Answer 3

Write it like a math equation.

let x = the first three digits of your phone number
let y = the last four digits

2. 80*x
3. 80*x + 1
4. (80*x+1)*250
5. (80*x+1)*250 + y
6. (80*x+1)*250 + 2y
7. (80*x+1)*250 + 2y - 250
8. [(80*x+1)*250 + 2y - 250] / 2

No use some algebra. Multiple the 250 through the (80*x +1) term

[20000x + 250 + 2y - 250] / 2

See the +250 & -250 can be combined to equal zero

[20000x + 2y] / 2

Divide both terms by two

10,000x + y

Remember, y is the last four digits of your number & x is the first three.

Multiply the first three digits by 10,000 doesn't change the actual digits, it just moves them.

Say your number is 321-4567

321 * 10,000 = 3210000 or 321-0000

So add the last four digits
3210000 + 4567 = 3214567
OR
321-4567

Simple

Answer 4

Assume your phone number is abc - efgh where a, b, c... are all digitss from 0 - 9

Ok -here is the equation you get from those steps

[250*(80*abc +1) + 2* efgh - 250]/2 some math here-

[250*80*abc + 2* efgh]/2 = 10,000abc +efgh

Now your calculator reads this as a,bc0,000 and efgh so you see on the display abcefgh

You could just as easily say multiply the first three digits by 10,000 and add the last four to get you phone number.

Answer 5

Let x be the first three digits and y the last four. Then, step by step we have

1. x
2. 80x
3. 80x + 1
4. 250(80x + 1)
5. 250(80x + 1) + y
6. 250(80x + 1) + 2y
7. 250(80x + 1) + 2y - 250 = 250*80x + 250 + 2y - 250 = 20000x + 2y
8. (20000x + 2y)/2 = 10000x + y

Now for any three digit number (like x) if I multiply that number by 10000 I will get that number with four zeroes at the end. When I add y to it, I get back the telephone number.

Example: telphone number = 982-3357. Then x = 982, y = 3357

10000*x = 9820000
10000*x + y = 9820000 + 3357 = 9823357, the telephone number!

Math Rules!

Answer 6

It's very simple.

Inverse functions are used, like adding "x" and then subtracting "x", or multiplying by "x" and then dividing by "x"; but in a more sophisticated way, for instants:

Multiplying the first 3 digits by 80 and then by 250 is like multiplying by 20,000 which is going to make room for placing the last four digits (twice just before dividing by 2), then you only need to divide by two in order to go back to the original number.

Let's say the number is 123-4567, then what really happens is "123" times 20,000 equals 2,460,000; plus 4567 times 2 equals 2,469,134; then if you divided by two is 1234567.

Adding "1" just before multiplying by 250 is nullified when you substract 250 (just to make it look more complicated).

Answer 7

Let x = the first 3 digits of your phone number.
Let y = the last 4 digits of your phone number.

Here's what the problem says to do algebraically, step by step.

1. x
2. 80*x
3. 80*x +1
4. (80*x +1)*250 = 20000*x +250
5. 20000*x +250 +y
6. 20000*x +250 +y+y = 20000*x +250 +2y
7. 20000*x +250 +2y -250 = 20000*x +2y
8. (20000*x +2y)/2 = 10000*x +y

Now, notice what 10000*x is. It is the first 3 digits of your phone number, followed by 4 zeros. When you add y -- the last 4 digits of your phone number -- they simply replace the zeros, resulting in your phone number.

I hope this is clear!

Answer 8

Let your phone number be abcdefg.

Then following your steps, we have:

(250(80abc+1)+defg+defg-250)/2
=(20000abc + 250 + 2defg -250)/2
=(20000abc + 2defg)/2
=10000abc + defg
=abcdefg

(Since multiplying by 10000 shifts the digits 4 to the left)

Answer 9

hate to demystify the "trick" but [ using a fav phone number 867-5309 with positions 123-4567 ] it works because once you key in the fiirst 3 digits of the number steps 2 thru 4 and step 7 do nothing more than multiply the 867 by 10,000 to push them clear of positions 4567 so the result is
867-xxxx or 8670000
steps 5, 6 & 8 double the last 4 digits and then half them again:
(5309 + 5309) / 2 = 5309
effectively leaving it intact so that when added you get:
8670000
+ 5309
------------
8675309

bingo!

Answer 10

tis is how it works
let the first 3 digits b x.
& last 4 digits be y.
now ur phone number is
10000*x+y.

now lets do the calculation u told.
1. x
2. x*80
3. x*80+1
4. (x*80+1)*250
5. (x*80+1)*250+y
6.(x*80+1)*250+2y
7. (x*80+1)*250+2y-250
8. {(x*80+1)*250+2y-250}/2
={20000x+2y}/2
=10000x+y
ie ur phone number