Sanderson M. Smith

NUMBER PUZZLE SENT BY PARENT
(Copy of letter I sent to Cate MailServe...Students & Parents)

Hi good people (PARENTS and STUDENTS)...

I was just sent this little puzzle (below) by the father of one of my students. (I refrain from using specific names on this MailServe.)

You may have seen puzzles like this. While I hadn't seen this particular one, I have seen similar one.

One can explain what seems to be the surprising result using basic algebra. The question WHY DOES THIS WORK? is easily resolved with MATH POWER.

The first part (below) is the puzzle just as it was sent by the Cate parent. I encourage you to follow the simple instructions and get the (perhaps surprising) result.

Then... I have attempted to display the simple algebra that shows why the result is really not that surprising.

I do encourage you to read through this and follow the basic instruction. It doesn't take long.

Here is the puzzle (as sent by parent)--->

Out for Dinner MATHEMATICS

This is pretty neat how it works out.

DON'T CHEAT BY SCROLLING DOWN FIRST

It takes less than a minute. Work this out as you read.

Be sure you don't read the bottom until you've worked it out!

This is not one of those waste of time things, it's fun.

 1. First of all, pick the number of times a week that you would like  to have dinner out. (try for more than once but less than 10) 2. Multiply this number by 2 (Just to be bold) 3. Add 5. (for Sunday) 4. Multiply it by 50 - I'll wait while you get the calculator... 5. If you have already had your birthday this year add 1752...  If you haven't, add 1751.... 6. Now subtract the four digit year that you were born.  You should have a three digit number ....  The first digit of this was your original number  (I.e., how many times you want to have eat out each week.) The next two numbers are .......... YOUR AGE! (Oh YES, it IS!!!!!) THIS IS THE ONLY YEAR (2002) IT WILL EVER WORK, SO SPREAD IT AROUND  WHILE IT LASTS.

OK... What follows is the MATH POWER explanation.

My responses are in caps and bold....

(Cate students... you are capable of doing this!) --->

1. First of all, pick the number of times a week that you would like  to

have dinner out. (try for more than once but less than 10)

**********

LET N = THE NUMBER, WHERE N = 2,3,4,5,6,7,8 or 9.

**********

2. Multiply this number by 2 (Just to be bold)

**********

OK, WE NOW HAVE 2N.

**********

**********

WE NOW HAVE 2N + 5.

**********

4. Multiply it by 50 - I'll wait while you get the calculator...

**********

DON'T NEED CALCULATOR FOR THE ALGEBRA.
WE HAVE 50(2N + 5) = 100N + 250

**********

**********

OK. LET'S ASSUME YOU HAVE HAD YOUR BIRTHDAY (AS I HAVE.. IN JUNE).

100N + 250 + 1752 = 100N + 2002

**********

6. Now subtract the four digit year that you were born.

**********

OK... CAREFUL HERE. HERE'S WHERE MATH POWER REALLY HELPS.

THE YEAR WILL BE OF THE FORM 19--, BUT THE LAST TWO DIGITS WILL VARY FROM INDIVIDUAL TO INDIVIDUAL. IN MY CASE, THE LAST TWO DIGITS WOULD BE 38 (I KNOW I LOOK YOUNG AND HANDSOME, BUT I REALLY WAS BORN IN 1938). HOWEVER, OTHERS WILL HAVE DIFFERENT VALUES OF T AND U. LET T = THE TEN'S DIGIT AND U = THE UNIT'S DIGIT. THEN A YEAR IN THE 1900'S CAN BE WRITTEN
1000 + 900 + 10T + U = 1900 + 10T + U.

OK... I'M NOW GOING TO FOLLOW THE INSTRUCTIONS WHICH SAY "SUBTRACT THE FOUR DIGIT YEAR THAT YOU WERE BORN."

100N + 2002 -(1900 + 10T + U)

OK, GOOD PEOPLE... CAN YOU SEE WHY THIS LITTLE PUZZLE "WORKS" FOR YOUR INDIVIDUAL VALUE OF T AND U, THE EXPRESSION 1900 + 10T + U IS SIMPLY THE YEAR YOU WERE BORN. IF YOU SUBTRACT THIS FROM 2002, YOU GET YOUR AGE (REMEMBER... WE'RE ASSUMING THAT YOU HAVE HAD YOUR BIRTHDAY IN 2002.) IF YOU ADD THIS TWO-DIGIT NUMBER (OR, IT COULD BE A ONE-DIGIT NUMBER IF AGE IS LESS THAN 10) TO 100N, YOU WILL HAVE A THREE-DIGIT NUMBER WHERE THE HUNDRED'S DIGIT IS N.

AS AN EXAMPLE, SUPPOSE I WOULD LIKE TO HAVE DINNER OUT 3 TIMES A WEEK (N = 3). SINCE I WAS BORN IN 1938 (AND IN THE MONTH JUNE... SO I HAVE ALREADY HAD MY BIRTHDAY IN 2002), MY VALUES OF T AND U (AS DEFINED ABOVE) ARE T = 3 AND U = 8. WITH THESE VALUES WE HAVE

100N + 2002 -(1900 + 10T + U)

= 100(3) + 2002 - [1900 + 10(3) + 8]

= 300 + (2002 - 1938)

= 300 + 64

= 364.

**********

You should have a three digit number ....

The first digit of this was your original number

(I.e., how many times you want to have eat out each week.)

**********

INDEED IT IS...SURPRISE, SURPRISE!

**********

The next two numbers are ..........

YOUR AGE! (Oh YES, it IS!!!!!)

**********

CORRECT AGAIN!

MY OBTAINED NUMBER WAS 364.

THE FIRST DIGIT (HUNDRED' DIGIT) IS 3, MY ORIGINAL NUMBER.

WOW!

THE LAST TWO DIGITS (64) REPRESENT MY AGE.

DOUBLE WOW!

(AS INDICATED ABOVE, THIS SURPRISES PEOPLE SINCE I APPEAR TO BE YOUNG, HANDSOME, HEALTHY-LOOKING, VIGOROUS, IN GREAT PHYSICAL SHAPE, A MARVELOUS PHYSICAL SPECIMEN, ETC., ETC., ETC.)

**********

THIS IS THE ONLY YEAR (2002) IT WILL EVER WORK, SO SPREAD IT AROUND  WHILE

IT LASTS.

**********

TRUE... BUT IT WOULD BE RELATIVELY EASY TO MAKE ADJUSTMENTS SO THAT "IT" WILL WORK IN ANY YEAR.

I ENCOURAGE YOU TO REVIEW THIS WONDERFUL LITTLE PUZZLE AND FIGURE OUT WHY IT WORKS IF YOUR BIRTHDAY IS, SAY, IN DECEMBER. YOU HAVE TO ADD SOMETHING OTHER 1752

**********

MATH POWER TO ALL (and you saw it at work here).

Doc

================

"Every new body of discovery is mathematical in form, because there is no other guidance we can have."

- CHARLES DARWIN