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Math Puzzle

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Strong Eagle
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Math Puzzle

Postby Strong Eagle » Mon, 22 Aug 2005 5:01 pm

Math puzzle.

In the sum shown below, each of the letters can be converted to a number. None of the first letters are zero. What are the numbers for each letter that solve the addition problem?


Image


Note that all the words/numbers are right justifed so that the 'F' in FIFTY is over the 'T' in STATES and the 'S' in STATES is over the 'M' in AMERICA, and the right most 'Y', 'S', and 'A' line up.

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Postby Saint » Mon, 22 Aug 2005 5:40 pm

Think I've got it but will give others a chance to work it out!

Very good one SE

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Postby sundaymorningstaple » Mon, 22 Aug 2005 6:10 pm

Same here, sent you PM

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Postby sapphire » Mon, 22 Aug 2005 9:34 pm

Lol, Iwas waiting for Saint to show up on this thread. He seems to relish these Math puzzles. So guys, out with it, what's the solution?
It's not getting any smarter out there. You have to come to terms with stupidity, and make it work for you.

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Postby Saint » Mon, 22 Aug 2005 9:49 pm

Bit unfair to post the solution so soon Sapphire, might be loads out there trying to solve it lol

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Postby sapphire » Tue, 23 Aug 2005 9:44 am

Hehe Saint, trust me, if they're anything like me, they gave up in less than 2 minutes. Anyway I can't stand Math. One of my friends once tried to convince me that Mathematics is one of the simplest things on earth. I think I've hated her since then. :lol:
It's not getting any smarter out there. You have to come to terms with stupidity, and make it work for you.

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Postby Strong Eagle » Tue, 23 Aug 2005 10:34 am

My next post contains the answer to the problem... so no peeking if you still want to work on it.

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(This space left intentionally blank)

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Postby Strong Eagle » Tue, 23 Aug 2005 10:39 am

The trick to this problem is to realize that the largest number that can be carried to the next column is 1. For example, since there are no two numbers that are the same being added together, the largest number that can be added up is 9 + 8 = 17, and with a carry from the previous column, the largest number is 18.

So, this means that A = 1 because S + something had to carry and 1 is the only thing that can carry.

Now, the only number that S can be to force a carry is 9, again because only 1 can be carried from the last column. And if S = 9, then M = 0 because 9 + 1 = 10.

So to recap to this point:
A = 1
S = 9
M = 0

So now we look at the right hand column, Y + S = A. From the numbers we have already, Y + 9 = 1, but since it can't be 1, it must be 11, so Y = 2 and we carry 1 to the next column.

So, now we have:

Y = 2
A = 1
S = 9
M = 0

4 numbers used up and 6 left to go.

Let's go back over to the left column where F + T = E. This has to be greater than 10 in order to carry to add 1 to S to get the A. Actually, since we have already determined 0, 1, and 2, it must be equal to or greater than 13, and E must be equal to or greater than 3.

Leaving out the four numbers already figured out, the only combinations for F + T that is greater than or equal to 13 are 5+7 (with a carry), 5+8, 6+7, 6+8, and 7+8.

Now it becomes a case of plugging in the combinations to see what works. We take a look at the second column from the right. With the carry, we know that T + E + 1 = C. So, we start using the pairs of numbers to get answers for E and C.

We start with F = 5 and T = 7 and assume a carry. Then E = F + T + 1 = 3. We plug that into T + E + 1 = C and get 7 + 3 + 1 = 11, or C = 1, but C can’t be 1 because we already know that A = 1. If we make F = 7 and T = 5 and try again, we get C = 9, and that won’t work either since we already know S = 9.

So, we try with F = 5 and T = 8. This time E = 3 or 4 with a carry. Then T + E + 1 = C becomes 8 + 3 (or 4) + 1 = 12 or 13 (C = 2 or 3). We know C cannot be 2 because Y = 2. So, maybe E = 4 and C = 3.

We move to the next column which is F + T = I. We know we have a carry so it is really F + T + 1 = I. Let’s plug in the numbers. 5 + 8 + 1 = 14, or I = 4. Whoops. I can’t be 4 because we already have E = 4.

We go back and check out the next set of numbers, 6 and 7. Turns out they don’t work either. The only set of numbers for F and T that work are 6 and 8. Once you use 6 and 8 for F and T it is easy to calculate the remainder of the puzzle and you get:

FIFTY
65682
STATES
981849
AMERICA
1047531

F = 6
I = 5
T = 8
Y = 2
S = 9
A = 1
E = 4
M = 0
R = 7
C = 3

stronger eagle

Re: Math Puzzle

Postby stronger eagle » Tue, 23 Aug 2005 11:22 am

ok i got the answer...its too bloody easy!


65682

981849

1047531

Strong Eagle wrote:Math puzzle.

In the sum shown below, each of the letters can be converted to a number. None of the first letters are zero. What are the numbers for each letter that solve the addition problem?


Image


Note that all the words/numbers are right justifed so that the 'F' in FIFTY is over the 'T' in STATES and the 'S' in STATES is over the 'M' in AMERICA, and the right most 'Y', 'S', and 'A' line up.

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Re: Math Puzzle

Postby Strong Eagle » Tue, 23 Aug 2005 12:03 pm

stronger eagle wrote:ok i got the answer...its too bloody easy!


So... quit whining and post something better.

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Postby coffeetea » Tue, 23 Aug 2005 12:30 pm

oh my oh my.. i almost fall asleep.. :roll: hahhaaa.... :lol:

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Postby Saint » Tue, 23 Aug 2005 4:19 pm

You would have explained the solution far better than me SE

Sapphire, Su doku is all the craze over here at the moment, you should give it a try and ou'll soon get addictive!!

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Postby sapphire » Tue, 23 Aug 2005 4:36 pm

This weekend I saw a book on Su Doku in Kinokuniya. Was intrigued, but not enough. I think I'm better off playing with colours. :D

Thanks for the solution SE!
It's not getting any smarter out there. You have to come to terms with stupidity, and make it work for you.


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