Birthday Trick

Ask your friend to do these calculations.
An example for 13th August, 1999 is shown at the right.

Multiply his/her date of birth by 20. (only date) 1320=260
Add 222. 260 + 222 = 482
Multiply by 5. 4825=2410
Add the birth month. 2410 + 8=2418
Multiply by 100. 2418100=241800
Add the last two digits of the birth year. 241800 + 99=241899
Add 111. 241899 + 111=242010
Ask him/her the answer and you will be able to say his/her date of birth.
Trick - Subtract 111111 (six 1s) from the answer. 242010-111111=130899
Separate the digits by twos. 13/08/99
That is the birth date (in the European format). 13th August, 1999.

Explanation of the Birthday Trick

Let D = Day born
Let M = Month born
Let Y = last two digits of the birth year

Multiply his/her date of birth by 20. 20D
Add 222. 20D + 222
Multiply by 5. 5 (20D + 222) = 100D + 1110
Add the birth month. 100D + 1110 + M
Multiply by 100. 10000D + 111000 + 100M
Add the last two digits of the birth year. 10000D + 100M + YY + 111000
Add 111. 10000D + 100M + YY + 111111
Trick - Subtract 111111 from the answer: 10000D + 100M + YY

Note: This trick gives you the date in the European form: DD/MM/YY

Ask your students to do the following:
Change this trick so that the answer comes out in the American format: MM/DD/YY

Here is the solution:

Let D = Day born
Let M = Month born
Let Y = last two digits of the birth year

Multiply his/her birth month by 20. 20*M
Add 222. 20M + 222
Multiply by 5. 5 (20M + 222) = 100M + 1110
Add the birth day. 100M + 1110 + D
Multiply by 100. 10000M + 111000 + 100D
Add the last two digits of the birth year. 10000M + 100D + YY + 111000
Add 111. 10000M + 100D + YY + 111111
Trick - Subtract 111111 from the answer: 10000M + 100D + YY