An EAsy Math Quiz.. but very interesting..

[Mahesh Kamdar]

Here is a simple Math Quiz.. I m sure eveyone will be glad to solve it logically..

 

Please replace the Alphabets in the following Math Sum, with intigers 1, 2, 3.... till 0.

 

S E N D

+ M O R E

________

M O N E Y

 

ENJOY !

MAHESH KAMDAR :eek:

[Tim_Lou]

do you mean like this?

_SEND

+MORE

______

MONEY

 

so that s and m are at the same digit place?

btw, do they have to be distinct?

[pgrmdave]

I've solved that before, but I don't remember how...and yes Tim, it should be right aligned.

[Tim_Lou]

well, actually there are many solutions... i wont spoil the fun here. the main thing is to realize the relationship between O and R, and the relationship between N and E.

[Mahesh Kamdar]

I've solved that before, but I don't remember how...and yes Tim, it should be right aligned.

 

To start with..the solution.. I have applied the following simple logical procedure..

 

M can not be other than 1, similarly O can not be other than 0... why?

Yes the simple logic is that even if we add the two degits with maximum values like 9 and 8 the total is 17, so M can not be more than 1. Similarly O can not be other than 0.. .

Now try presumimg the values of E, or N.. and slowly we may reach the solution. There are more than one answers for this quiz.

Thanks and Regards

Mahesh Kamdar:steering:

[Mahesh Kamdar]

do you mean like this?

_SEND

+MORE

______

MONEY

 

so that s and m are at the same digit place?

btw, do they have to be distinct?

 

Yes you are right there are at the same digit place.

 

Mahesh Kamdar :confused:

[Mercedes Benzene]

I think I've found the answer....

Am I supposed to post it here??

[cwes99_03]

Better to post the method, so your method can be understood and each person can find the answer themselves.

[cwes99_03]

SEND + MORE = MONEY

 

D+E=Y or 10+Y

N+R=E or 10+E, or N+R+1=E or 10+E

so on and so forth to find the answer.

[Mercedes Benzene]

To find the answer, I used a method simliar to what cwes just describes, but I used basic algebra (solving for an unknown) where each letter represented a different variable. I then assigned an arbitrary value for one of the letters and worked from there.

I always have a hard time describing things like this... sorry, but hopefully this may give you an idea as to how to solve it.

[arkain101]

I don't get the question.

 

Replace letters with what?

 

Can you explain it better..

[ughaibu]

See also this thread: http://hypography.com/forums/watercooler/6040-alphametic-poems.html?highlight=alphametic

[Mercedes Benzene]

Okay....

Maybe this will help a little bit.

 

If you look at the word "equation" you see that both terms are smaller than the sum (money). This means that if you look at the left-most letters in the 2terms "S" and "M" (no pun intended:lol:), then they must equal "MO" in money.

So, an arbitrary value to the "M" in MORE. 1 is a good value to use. Since the "MO" in money is 2 digits, then you must expect "MO" to equal 10 because each letter must be assigned a specific number. If that is the case, then "what" + "M" = 10? Since we have already declared "M" as 1, then 9 + "M" = 10. That makes S = 9 and M = 1.

Continue one doing the same thing, applying the basic rules of addition and subtraction.

Use algebra to confirm all of your deductions (eg: "N" = "N").

Note: I decided to get more complex with my algebraic analysis, but I do not want to confuse you all any more than I probably already have :hihi:

I'm sure there is some simpler way of doing it than I have, but I always seem to over-complicate things!

 

GOOD LUCK>>

[cwes99_03]

Well you might like to say S = 9 but s could = 8. However, M must = 1 since no two single digit numbers when added together can be greater than 18.

 

Thus your first deduction that M = 1, is the only valid answer for that letter.

[cwes99_03]

I don't get the question.

 

Replace letters with what?

 

Can you explain it better..

 

:hihi: Sorry, Arky, I can't resist. Why doesn't the above surprise me?

[Mercedes Benzene]

Gah! I am horrible at explaining things....

I thought I would be able to help.... :shrug:

[cwes99_03]

OK, Mercedes, I'll give it a slightly better shot.

 

1) each letter in the word puzzle represents a number 0-9. Add each column together to figure out which number each letter represents.

 

2) M=1; as stated above no two single digit numbers (since there are only two lines to be added together, there can only be two numbers added together in each column) when added together can equal greater than 18 (9+9=18). Even if you carry a one from the previous column, the greatest value for the MO in money is 18 (1+9+8=18 since the S and the M cannot each be 9.) M however cannot be 0 because it then would be a valueless place holder in front of the chain of letters (01923 is not a real integer it is a string value).

 

3) Once M is determined to be 1, S+M (bit of letter fun here S+M=S and M) must be at least 9, so that a carried 1 when added to S+M would make 1+S+M =10. This leaves S ={8 or 9}. (Note I didn't say that 1+S+M could not be 11 yet.) MO cannot be equal to 11, because M cannot be equal to O (that's an o not a 0). Thus if there is a carried 1 from the addition of the previous column S=8. If there isn't a carried 1 then S=9.

 

4) We now have eliminated three numbers from our pool 0,1,2,3,4,5,6,7,8,9. (One of the two magenta numbers has been eliminated but we aren't sure which. We will be using 8 of 10 numbers.) Did you see how we eliminated 0? Hint: S+M cannot be 11.

 

5) Now to the next column E+O=E, right? Since E is a single digit number, then there is no 1 carried from the this column to the next. This firms up our answer to S=?. Now if you have E+O=N on your chart good for you. This means that N=E+1. The 1 comes from the addition of N+R>10 (not >= because we've already assigned 1 and 0 to other letters.)

 

6) N+R=10+E. E+1=N. 1+E+R=10+E or R=9. Sorry folks, that's wrong we've already deduced that S=9. Therefore R=8. (Can you figure out how? Read on.)

 

7) D+E>11. Therefore 1+N+R=10+E. Now we also know that y>1 (but we already knew that because 0 and 1 are already used. (Used numbers so far are 0,1,8,9.)

 

8) Since E+1=N and D+E=10+Y then D+N-1=10+Y or D+N-11=Y.

 

9) Y=2, D=7, N=6, E=5. (OK, so I left you a bit of leg work here at the end, but it shouldn't be too hard. I'll edit this in 24 hours in a new post to show the missing steps.