Basic Addition with a twist: THREE + FIVE = EIGHT

A

alphabetagamma

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In this arithmetic problem, distinct letters represent distinct digits in base 10. Find digit values for which the addition is correct or prove that there is no such assignment of digit values:
T H R E E
+_F I_V E
E I G H T

underscores are used to try and get it to line up right

Fun problem to hand out when you feel like shutting somebody up for a few minutes.
 
alphabetagamma said:
... underscores are used to ... get it to line up ...
Click to expand...


Hello ? ? ?:

The [ code ] tags provide both a fixed-width font and space-striping suppression.

Code: 
    T H R E E
      F I V E
+   ---------
    E I G H T

Use the Preview button to see any adjustments needed.

Cheers,

~ Mark :)

 
Code: 
T H R E E
+ F I V E
---------
E I G H T
Are you sure you copied this correctly? I don't believe it has any solution. :oops:

On the other hand, the following additions are solveable:

Code: 
ONE + FOUR = EIGHT (four solutions)
TWO + FOUR = EIGHT (four solutions)
TWO + SEVEN = EIGHT (four solutions)
THREE + FOUR = EIGHT (twenty-two solns)
THREE + SEVEN = EIGHT (six solutions)
THREE + ZERO = EIGHT (ten solutions)
FOUR + FIVE = EIGHT (twenty solutions)
Code: 
FOUR + NINE = EIGHT (thirteen solutions)
FOUR + ZERO = EIGHT (twenty-eight solns)
FOUR + TEN = EIGHT (four solutions)
FIVE + SEVEN = EIGHT (seventeen solns)
FIVE + NINE = EIGHT (nine solutions)
FIVE + ZERO = EIGHT (twelve solutions)
NINE + ZERO = EIGHT (twenty-four solns)
Eliz.
 
Having everything equal to zero is a possible solution for any problem like this. Solving by hand, I got one other solution. I didn't bother to look for any other solutions besides the one I got and everything equal to zero though. But it does have at least 2 solutions.
 
In this arithmetic problem, distinct letters represent distinct digits in base 10
Click to expand...

According to above condition - all zero is not a solution.

Can you please share your solutions with us.
 
stapel said:
... Are you sure you copied this correctly? I don't believe it has any solution ...
Click to expand...


Ah, Elizabeth is one sharp lady. I entered this puzzle into the "solver" at the web site which Denis posted above.

That software is also unable to find a solution. (Unless the "solution" is to find a way to get those people to shut up forever!)

~ Mark :)

 
alphabetagamma said:
80999
+9009
90008

Doesn't that work?
Click to expand...


You asked if your example does not work.

The answer to that question is "Yes".

The reason why your example does not work is obvious.

 
Wow, I should learn to read. Orrrr I could just change the original question to fit my answer, haha wish I could do that on exams.
 
alphabetagamma said:
distinct letters represent distinct digits in base 10....
80999
+9009
90008

Doesn't that work?
Click to expand...
Your solution will "work" only if you view E, F, and R as being the same one letter (that is, as being non-distinct letters, actually the same as each other), and G, H, I, and V as all being the same some-other letter. In other words, only if you view E, F, G, H, I, V, and R as actually representing only two distinct characters.

Of course, I (and "Big Bird", et al) could be completely mistaken....

Eliz.
 
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