how does TEACH + MATH = GIFTED

Question

This is a problem solving problem where each of the letters equals a number

Answer 1

First, read and re-read the problem until you understand it and can put it into your own words.  Then, collect your observations:

      - each letter-number combination is unique

              (no letter can have two numbers; no number assigned to two letters)

     - to have T=0 or M=0 or G=0 doesn’t make sense (disallow leading zeros)

     - (you might have some more)  (note: With some guidance, Justin R. might become a great thinker.)

 

Write the problem as a simple addition problem and make more observations:

     T  E   A  C  H        

+      M  A  T  H

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

  G  I  F  T  E  D

 

 2H = 0D or 1D    (note: even if H=9, D=18)

    D must be even, that is: 0, 2, 4, 6, or 8

G=1    (note:  even if T=9, there won’t be a carry more than 9, so G=1)

       But, if T is not 9 then the carry must be larger.

2A = xT  or else 2A+carry = xT

T must also fill a role in MATH and GIFTED  (this looks important)

E must fill roles in both TEACH and GIFTED (this is also important)

The only other important letter (used twice) is the E.

 

Now, ordering you observations makes the problem easier or harder (this often comes with experience, but I’d say that thinking outdoes experience most days).  Which order eliminates most of the rest of the options:

     -  T<>0 and M<>0 and G<>0

    -   G=1   (and none of the other letters are 1)

   . . .

 

And, it is very, very useful to keep a translation table (not is above; known is below):

   T

   M

   G

   0   1   2   3   4   5   6   7   8   9

        G

 

 

   0                          0    0

   T   E   A   C   H   M   G   I   F   D         [these are all the letters]

                                     1

   

2H equals either 0D or 1D, so D is even: either 0 ,2 ,4 , 6, or 8

 

There are lots of rules of simple addition (for a positional number system) that involve carries (so important that you might want to invent  w,x,y, and z and put them above the columns in this problem), even and odd numbers, etc.  We already eliminated leading zeros.  Now, uniqueness of values becomes the constraining (limiting) force.

 

The important value of this problem is not in getting the right answer!  It is in knowing the rules of addition, knowing the rules of logic (e.g., if it is not this then it must be that), and keeping an organized record of your progress (that is essential!).

 

So, PLZ develop those skills.

 

However, there is only one answer:

 

    T  E  A  C  H             9  7  4  8  3

       M  A  T  H                 5  4  9  3

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

G  I   F  T  E  D         1  0  2  9  7  6

Answer 2

Hmm I never saw this problem before! Well since each letter equals a number, we can assume T in TEACH and MATH is the same number, as well as the H and the A. So maybe we can factor these out and see if that helps?

 

TEACH + MATH = GIFTED 

 

can be rewritten as:

 

TAH(EC + M) = GIFTED

 

Then we can try dividing both sides by T which gives us 

 

AH(EC + M) = GIFED

 

I'm stuck after that lol. I'll do some research though! I would also try choosing some simple numbers for each letter and seeing what happens?