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Mrs Bissli
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Thu, Oct 03 2013, 6:26 pm
Each alphabet letters in the four-digit addition below represent different numbers.
Can you figure out which letter is which number? Explain the logic
(BTW there are more than one correct answers.)
F O U R
+ F I V E
------------
N I N E
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imasinger
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Thu, Oct 03 2013, 6:38 pm
Mrs Bissli wrote: | Each alphabet letters in the four-digit addition below represent different numbers.
Can you figure out which letter is which number? Explain the logic
(BTW there are more than one correct answers.)
F O U R
+ F I V E
------------
N I N E |
Here's a start.
R must =0, since R+E=E, and that doesn't work for any other case.
There are 8 of the 10 digits from 0 to 9 in this problem.
E, therefore, must be one of those single digits. Actually, E can be any of the 3 digits that do not fit elsewhere.
I'll keep more to myself fora bit.
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DrMom
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Thu, Oct 03 2013, 6:46 pm
F<5, since the sum is only 4 digits.
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Mrs Bissli
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Thu, Oct 03 2013, 7:00 pm
getting warmer!
imasinger, you got R right.
(I confess this was my 11yo DD's "bonus" math homework.)
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sequoia
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Thu, Oct 03 2013, 7:09 pm
I'm confused. If O + I = I, wouldn't O be 0?
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imasinger
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Thu, Oct 03 2013, 7:14 pm
sequoia wrote: | I'm confused. If O + I = I, wouldn't O be 0? |
Not if the previous two numbers totalled more than 10, so that a 1 was carried.
(Confession: I have figured at least 1 correct answer for this. Second confession: I may have seen it before, many years ago, as it looks like it is from the Wayside School math fun book.)
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Hashem_Yaazor
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Thu, Oct 03 2013, 7:59 pm
2970+
2483
____
5453
Does that work?
My logic was this, BTW:
Set R = 0.
E can be anything, leave it to the side.
U+V needs to be higher than 10 so it can carry over a 1 which means if you set O to 9 and add that 1, the I underneath it will equal the same value as the I in the sum.
The 1 carries over to the F's, which mean 2Fs + 1 = N.
Oh, forget it, I can't explain more, too tired.
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Mrs Bissli
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Sat, Oct 05 2013, 12:54 pm
Yes HY, you've got it (or one of several combos that work!)
And your explanation is correct, if not complete.
There is one more explanation for identifying N.
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imasinger
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Sun, Oct 06 2013, 1:21 pm
I identified N the same way, but filled in some of the other numbers differently.
2980
2176
_____
5156
I can't think of the other way to consider N, though!
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Mrs Bissli
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Sun, Oct 06 2013, 2:27 pm
Hint: there are possibly two numbers that can be N.
And as HY said, N is an odd number because 2F +1 =N.
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