Solution by Jeremy Greene what's really going in this algorithm is that it multiplies the first three digits of your phone number by 10,000 and then just adds the last four digits in. check it out! let your phone # = abcdefg 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) abc 3. Multiply by 80 (abc)(80) 4. Add 1 (abc)(80)+1 5. Multiply by 250 [(abc)(80)+1]250 = (abc)(20,000)+250 6. Add the last 4 digits of your phone number (abc)(20,000) + 250 + defg 7. Add the last 4 digits of your phone number again. (abc)(20,000) + 250 + defg + defg = (abc)(20,000) + 250 + 2defg 8. Subtract 250 (abc)(20,000) + 250 + 2defg - 250 = (abc)(20,000) + 2defg = 2[(abc)(10,000)+defg] (i factored a 2 out in that last step) 9. Divide number by 2 2[(abc)(10,000)+defg]/2 = (abc)(10,000)+defg = abc0000+defg = abcdefg showing that last step in a clearer way: abc0000 + defg ---------- abcdefg Do you recognize the answer? yes, it's the original phone number!