Please explain the math behind this (in the details section) and why does it work?

Question

1. Key in the first three digits of your phone number (NOT the Area code...)
2. Multiply by 80
3. Add 1
4. Multiply by 250
5. Add to this the last 4 digits of your phone number
6. Add to this the last 4 digits of your phone number again.
7. Subtract 250
8. Divide number by 2

Do you recognize the answer ??

Answer 1

Let's call x the first three digits and y the last four digits.

(((x* 80 + 1) * 250 + 2*y) - 250)/2 is what you're computing

(20000x + 250 + 2y - 250)/2

(20000x + 2y)/2

10000x + y

So, you're shifting x over by four and adding in y.

That's why.

Answer 2

We will use 2458975
1. Key in the first three digits of your phone number (NOT the
Area code...)

2. Multiply by 80
245 * 80 = 19600

3. Add 1
19600 + 1 =19601
4. Multiply by 250
4900250
5. Add to this the last 4 digits of your phone number
Let's use 8975
4909225
6. Add to this the last 4 digits of your phone number again.
4918200
7. Subtract 250
4917950
8. Divide number by 2
2458975

OK, here is why it works
Let the phone number be ABCDEFG

Key in the 1st 3 digits
What is displayed =
100A + 10B + C

Multiply by 80
8000A + 800B + 80C
Add 1
8000A + 800B + 80C + 1

Multiply by 250
2000000A + 200000B + 20000C + 250

Add the last 4 digits
The last 4 digits will equal 1000D + 100E + 10F + G
to get
2000000A + 200000B + 20000C + 250 + 1000D + 100E + 10F + G
Add the last 4 digits again
2000000A + 200000B + 20000C + 250 + 2000D + 200E + 20F + 2G
Subtract 250
2000000A + 200000B + 20000C + 2000D + 200E + 20F + 2G
Divide by 2
1000000A + 100000B + 10000C + 1000D + 100E + 10F + 2G

So the calculator displays
ABCDEFG which is the phone number

Answer 3

It only works when there is a 4 digit area code leaving 7 for the maths. I first used my mobile number (starting with 008) and ended up with 88686. My number ends 008686. I then used my home number and got 7500328, which is wrong again.

Answer 4

Call the first three digits of yur phone number a and the last 4 digits b. That means you'd write the number as 10000a + b.
Then
((((80a + 1)*250) + 2b) - 250)/2 = 10000a + b
Do the algebra ☺

Doug

Answer 5

Let ABC = the first three digits of your phone number and WXYZ = the last four digits. Then, write the equation for the instructions you provided:

((((ABCx80)+1)x250)+
WXYZ+WXYZ-250)/2

Simplifying:

(80x250xABC+250+2xWXYZ-250)/2

(20000xABC+2xWXYZ)/2

10000xABC+WXYZ = ABCWXYZ

Multiplying ABC by 10000 just shifts it to the left so when you add WXYZ, you end up with the numbers in sequence. No real mystery. Just math.

Answer 6

Just turn it into an algebra question :)
Let's say your phone number is a 7 digit number ABCDEFG. Now let's apply those steps to this number.
1. ABC
2. 80*ABC
3. 80*ABC + 1
4. 250*[80*ABC + 1] = 20,000*ABC + 250 = 2*ABC0000 + 250
5. 2*ABC0000 + 250 + DEFG
6. 2*ABC0000 + 250 + 2DEFG
7. 2*ABC0000 + 2DEFG
8. ABC0000 + DEFG = ABCDEFG

Answer 7

phone number = "abcdefg"
1. "abc"
2. 80*"abc" = 8*"abc0"
3. 8*"abc0" + 1
4. 250 * (8*"abc0" + 1) = 2*"abc0000" + 250
5. 2*"abc0000" + 250 + "defg"
6. 2*"abc0000" + 250 + 2*"defg" = 2*("abc0000" + "defg") + 250
= 2*"abcdefg" + 250
7. 2*"abcdefg"
8. 2* "abcdefg"/2 = "abcdefg"

Answer 8

PMP gave you the explanation you're looking for.

Answer 9

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