Math Homework Help-Urgent?

Question

1) In the following, different letters represent different digits. What digit does the letter O represent?

ONE + OUR = FIVE

ONE x 4=FOUR


2) Each of 10 cards displays two different letters (A,B,C,D, or E) one on the front and other on the back. The front of each card is shown. No two cards have the same pair of letters. What is the fewest cars you can turn over and be absolutely sure that an E will appear?

A A A A
B B B
C C
D



I'd like explanations too if possible

mathgirl · Accepted Answer

I wasn't able to solve the first question as it was written, but if it is rewritten as:

ONE + FOUR = FIVE
ONE x 4 = FOUR

Then here's all the numbers:
E = 5
F = 1
I = 7
N = 4
O = 3
R = 0
U = 8
V = 2

So you get:

345 + 1380 = 1725
345 x 4 = 1380

I'm sure there's a better way to solve it than I did, because I basically just looked at the equations and tried a bunch of different numbers until I found a set that worked.  Not very scientific, but it works if you have all day. ;)  (For example, since 4xE=something ending in R and E+R=some number ending with E, the only numbers that would work were E=5 and R=0.  Along the same lines for the rest.)

The second problem is a bit easier:  Since you know what's on the front of all the cards, and that all the letters on the back are different from the letters on the front, and that no two cards have the same set of letters, you know what is on the back of all the cards:

There are 4 cards with an A showing, and only 4 other letters that can be on the back, so you know that they are:

A/B, A/C, A/D, and A/E

Now there are 3 cards with a B showing, and you already have A/B, so those are:

B/C, B/D, and B/E

Same for the C's:

C/D, and C/E

And that leaves:

D/E

So you only have to flip over one card to be absolutely sure that an E will appear, because you know for sure that the card with a D on top has an E on the back.  

Hope that makes sense.

Math Homework Help-Urgent?

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