Math trick? Can anyone explain the logic behind this...?

Question

1. Grab a calculator. (you won't be able to do this one in your head)
2. Key in the first three digits of your phone number (NOT the area code)
3. Multiply by 80
4. Add 1
5. Multiply by 250
6. Add the last 4 digits of your phone number
7. Add the last 4 digits of your phone number again.
8. Subtract 250
9. Divide number by 2

Do you recognize the answer?


... how did that happen?

Answer 1

Easy! Here's how:

Suppose your number is xy where x represents the first 3 digits and the y represents the last 4 digits.

The steps give

3: 80x
4: 80x + 1
5: 250*(80x + 1) = 2000x + 250
6: 20000x + 250 + y
7: 20000x + 250 + 2y
8: 20000x + 2y {we took 250 away}
9: 10000x + y

10000x gives you x with four zeros at the end, so, when you add y, the four digits of y replace the zeros - so you end up with your phone number again !

Answer 2

Phone Number Math Trick

Answer 3

Hi,

Step 1 Calculator in hand - ready to go
On step 2, lets call the first 3 digits of your phone number "x".
On step 3, when you multiply by 80, It would be 80x.
On step 4 when you add 1, it would be 80x + 1
For step 5 when you multiply by 250, it would be 250(80x + 1) which multiplies together to become 20,000x + 250
If we call the last 4 digits of your number "y" then when we add them in step 6 we get 20,000x + 250 + y
Step 7 adds "y" again to give 20,000x + 250 + 2y
Step 8 subtracts the 250 away to get 20,000x + 2y
Step 9 divides by 2 to get 10,000x + y.

Multiplying a number by 10,000 moves the number over 4 places to the left with 4 zeros behind it. Those 4 zeros make places to add in the last 4 digits of your 'you-know-what", your phone number. So if my phone number was 588-5026, I'd get

Step 2 => 588
Step 3 => 588 * 80 = 47040
Step 4 => 47040 + 1 = 47041
Step 5 => 250 * 47041 = 11760250
Step 6 => 11760250 + 5026 =11765276
Step 7 => 11765276 + 5026 =11770302
Step 8 => 11770302 - 250 = 11770052
Step 9 => 11770052/2 = 5885026

It will work for anyone's number. It's a simple math pattern.

I hope that explains how it happened!

Answer 4

The only formula that I could think of would be as follows:

let a = the first 3 digits of the phone number
let b = the last 4 digits of the phone number

since a, the first 3 digits, precedes b, the last 4 digiits, by four place values, the phone number would then be = 10,000a + b

[(80a + 1)250 + 2 - 250] / 2 =

[20,0000a + 250 + 2b - 250] / 2 =

[20,000a + 2b] / 2 =

10,000a + b (which is the phone number in question)

Answer 5

Step 3 and 5: 80 X 250 = 20000, this is what you multiply the first 3 numbers by.

Step 6 and 7: Add the last 4 numbers twice

Step 4, 5 and 8: add 1, multiply by 250 subtract 250 = 0

Step 9: divide twice your phone number by 2

Answer 6

x=First 3 digits of phone no. (I think it should be 4 cos with 3 1 number was missing in the end)

y=Last 4 digits of phone no

(250(80x+1)+2y-250)/2= Your Phone No. !
(20000x+250+2y-250)/2= Your Phone No. !
(20000x+2y)/2= Your Phone No. !
10000x+y= Your Phone No. !

Kinda complicated eh (but give it a shot it works)

Basically you divide by 2 because you added the last 4 digits of phone no. 2 times (same as multiplying the last 4 digits by 2). I am not exactly sure why, but I guess if you show the algebraic working to your teacher, they should accept it as an answer and mention why you divide by 2.

Sorry but I am not exactly sure why you do such things e.g. subtract 250 (doesn't oppose multiplying by 250).

Hope the algebra makes sense and is useful!

Cya

From ????

Answer 7

Let the phone number be abcdefg. Then following the algorithm at each stage:

2. abc
3. abc x 80
4. (abc x 80) + 1
5. (abc x 20000) + 250 = (abc0000 x 2) + 250
6. (abc0000 x 2) + 250 + defg
7. (abc0000 x 2) + 250 + (defg x 2)
8. (abc0000 x 2) + 250 + (defg x 2) - 250 = (abc0000 x 2) + (defg x 2)
9. [(abc0000 x 2) + (defg x 2)] / 2 = abc0000 + defg = abcdefg.

Hence, you always end up with your phone number.

Simple, eh?

Answer 8

Let's define 1st 3 digits as a,b,c. To make it a 3-digit number it should be defined as 100a+10b+c

Last 4 digits will then be d,e,f,g or:
1000d+100e+10f+g

SO......

Steps 2,3,4: 80(100a+10b+c)+1
Step 5: 20,000(100a+10b+c)+250
Steps 6,7: 20,000(100a+10b+c)+250+2000d+200e+20f+2g
Step 8: 20,000(100a+10b+c)+2000d+200e+20f+2g
Step 9: 1,000,000a+100,000b+10,000c+1000d+100e+10f+g

Yeah - it's gonna look familiar....

Answer 9

I'm not very good at math but I can tell you that is a very neat trick!

Answer 10

I dunno how it works, but its pretty impressive