A Math Question for a friend?

Question

My friend's daughter is in Geometry...They gave her a Math question, more like a "Birthday Trick"...

She didn't have the worksheet, just her daughter's work....

It's hard without the actual steps but her birthday is 10/25/90

And this is her work....

10

x 4

------

40

+13

------

53

x 25

--------

265

+1060

-----------

1325

- 200

----------

1125

+ 25

----------

1150

+1150

----------

2300

- 40

----------

2260

x 50

---------

113,000

+ 90

------------

113,090

- 10,500

--------------

102,590 = 10/25/90

The teacher is asking her to explain how this formula works, or why it works, can someone please help her out!

Thanks ;)

Answer 1

If you try a different set of numbers for someone's birthday it should work out the same for those numbers also.  It is one of those problems that the numbers you use in the equation, those numbers will always come back out in the answer.  Try it with another set of numbers to see.

Answer 2

Given Month/Date/TwoDigitYear ==> M/D/Y

Steps:

1. Multiply the month number (M) by 4.

2. Add 13.

3. Multiply again by 25.

4. Now subtract 200 from the last result.

5. Add the date number (D).

6. Multiply the last result by 2.

7. Subtract 40.

8. Multiply the last result by 50.

9. Add the last 2 digits of year.

10. Subtract 10,500.

This is what you are doing with the math....

Formula = ( 50 x [ 2 x { 25 [ (4 x Month) + 13 ] - 200 + Day} - 40 ] ) + TwoDigitYear - 10,500

I know the above formula looks complicated and messy, so let me break the steps down for you....

Formula broken down by steps:

1. Multiply the month number (Month) by 4.

==> 4 x Month

2. Add 13.

==> (4 x Month) + 13

3. Multiply result in "Step 2" by 25.

==> 25 x [ (4 x Month) + 13 ]

........ = (25)(4 x Month) + (25)(13) = (100 x Month) + 325

4. Now subtract 200 from the last result.

==> [ (100 x Month) + 325 ] - 200

........ = (100 x Month) + 325 - 200 = (100 x Month) + 125

5. Add the date number (Day).

==> [ (100 x Month) + 125 ] + Day

6. Multiply the last result by 2.

==> { [ (100 x Month) + 125 ] + Day } x 2

........ = [ (100 x Month) + 125 + Day ] x 2

........ = (100 x Month)(2) + (125)(2) + (Day)(2)

........ = (200 x Month) + 250 + (2 x Day)

........ = (200 x Month) + (2 x Day) + 250

7. Subtract 40.

==> [ (200 x Month) + (2 x Day) + 250 ] - 40

........ = (200 x Month) + (2 x Day) + 250 - 40

........ = (200 x Month) + (2 x Day) + 210

8. Multiply the last result by 50.

==> [ (200 x Month) + (2 x Day) + 210 ] x 50

........ = (200 x Month)(50) + (2 x Day)(50) + (210)(50)

........ = (10,000 x Month) + (100 x Day) + 10,500

9. Add the last 2 digits of year to previous result.

==> [ (10,000 x Month) + (100 x Day) + 10,500 ] + TwoDigitYear

10. Subtract 10,500 from previous result.

==> { [ (10,000 x Month) + (100 x Day) + 10,500 ] + TwoDigitYear } - 10,500

...... = (10,000 x Month) + (100 x Day) + 10,500 + TwoDigitYear - 10,500

...... = (10,000 x Month) + (100 x Day) + (10,500 - 10,500) + TwoDigitYear

...... = (10,000 x Month) + (100 x Day) + 0 + TwoDigitYear

...... = (10,000 x Month) + (100 x Day) + TwoDigitYear

...... = 10,000M + 100D + Y <== where Y is the TwoDigitYear

So all those tedious math steps that are in your friend's daughter's above math work all finally comes down to the basic Birthdate Formula of...

BIRTHDATE = 10,000M + 100D + Y

That's why it works.... and the way the formula works is how I explained it above.....  All those mathematical operations of adding and multiply and subtracting is the same as the simple equation "BIRTHDATE = 10,000M + 100D + Y" after you've manipulated the numbers.....

Okay.... Let's say that your birthday is 12/31/2002

So... M = 12 ... because December is the 12th month...

..... and D = 31.... because the date is 31st

..... and Y = 02... because you take the last two digits of 2002

BIRTHDATE = 10,000M + 100D + Y

...................... = (10,000)(12) + (100)(31) + 02

...................... = 120,000 + 3,100 + 02

...................... = 123,102 ==> which translates to 12/31/02 =)

The example birthday was... 10/25/90....

Okay....

So here... M = 10 ... because October is the 10th month...

..... and D = 25.... because the date is 25th

..... and Y = 90... because you take the last two digits of 1990

BIRTHDATE = 10,000M + 100D + Y

...................... = (10,000)(10) + (100)(25) + 90

...................... = 100,000 + 2,500 + 90

...................... = 102,590 ==> which translates to 10/25/90 =)

Okay.... my birthday is 2/15/1974

So... M = 2 ... because February is the 2nd month...

..... and D = 15.... because the date is 15th

..... and Y = 74... because you take the last two digits of 1974

BIRTHDATE = 10,000M + 100D + Y

...................... = (10,000)(2) + (100)(15) + 74

...................... = 20,000 + 1,500 + 74

...................... = 21,574 ==> which translates to 2/15/74 =)

Now try your birthdate.... you'll see that it works.....

M is the month #.... so can be 1,2,3,4,5,6,7,8,9,10,11,12

D is the date..... so can be any number 1-31

Y is are the last two digits of the year... so can be any number 00-99 ... 00 is used for the year 2000