Phone number algebra
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?
Explanation
Let your phone number be abc-defg.
In expanded base-10 notation, this number can be written as
1,000,000*a + 100,000*b + 10,000*c + 1000*d + 100*e + 10*f + 1*g.
This is the key information. Do you see it?
2. Key in the first three digits of your phone number, abc
abc can be written in expanded notation as
100*a +10*b +c
3. Multiply by 80.
(100*a +10*b +c)*80
4. Add 1.
(100*a +10*b +c)*80 +1
5. Multiply by 250
((100*a +10*b +c)*80 +1)*250
6. Add the last four digits of your phone number.
The last four digits, defg, can be written in expanded notation as
1000*d + 100*e + 10*f + 1*g. Adding it to what we have above, we have:
((100*a +10*b +c)*80 +1)*250 + 1000*d + 100*e + 10*f + 1*g
7. Add the last 4 digits of your phone number again.
((100*a +10*b +c)*80 +1)*250 + 1000*d + 100*e + 10*f + 1*g + 1000*d + 100*e + 10*f + 1*g
8. Subtract 250.
((100*a +10*b +c)*80 +1)*250 + 1000*d + 100*e + 10*f + 1*g + 1000*d + 100*e + 10*f + 1*g - 250
9. Divide the number by 2.
[((100*a +10*b +c)*80 +1)*250 + 1000*d + 100*e + 10*f + 1*g + 1000*d + 100*e + 10*f + 1*g - 250]/2
Now simplify:
[(8000*a + 800*b + 80*c + 1)*250 + 2000*d + 200*e + 20*f + 2*g -250]/2
(now divide by 2)
= (8000*a + 800*b + 80*c + 1)*125 + 1000*d + 100*e + 10*f + 1*g -125
= 1,000,000*a + 100,000*b + 10,000*c + 1000*d + 100*e + 10*f + 1*g +125 -125
= 1,000,000*a + 100,000*b + 10,000*c + 1000*d + 100*e + 10*f + 1*g
This is exactly your phone number written in expanded notation!