Math Is Fun Forum

dino

Member

Registered: 2008-03-07

Posts: 1

letter number problem

Need help solving this problem please

Each letter stands for a different digit.
If WAIT = 8472,
What number does STOP represent?

Given

        GO
+  SLOW
------------
    STOP

Thanks

eclipse4227

Member

Registered: 2007-04-23

Posts: 10

Re: letter number problem

hmm, so you mean that each letter can be replaced by a number?
and can a digit be used twice, for instance, L=2 and T=2?

Last edited by eclipse4227 (2008-03-07 14:02:12)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: letter number problem

and can a digit be used twice, for instance, L=2 and T=2?

Each letter stands for a different digit.

There better be a carry to the 3rd (from the right) column, otherwise L = T.  So G + O + carry_1 > 9, where carry_1 is the carry from the first (from the right) column.  This in turn implies that either G or O (or both) are >= 5.  This also implies that L + 1 = T.  Furthermore, L < 9 since the carry of L + 1 = T > 10 implies that S = S + 1, which is certainly false.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: letter number problem

So G + O + carry_1 > 9, where carry_1 is the carry from the first (from the right) column.

Furthermore, G + O + carry_1 > 9 + O, meaning G + carry_1 > 9 and so G must be equal to 9.
You also know the value of T and so can say L + 1 = 2 in your second statement. Combined with the no-carry reasoning, that shows that L=1.

Now we have:

        9O
+  S1O8
----------
    S2OP

and free digits 0, 3, 5, 6. The first column (from the right) has a carry, so O+8 = P+10.
Therefore O = P+2. The only digits available that satisfy this are 3 and 5.

Now only 0 and 6 are left free, but assuming a number cannot begin with 0, that restricts S to equal 6.

Final answer:

        95
+  6158
----------
    6253

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Why did the vector cross the road?
It wanted to be normal.