Hi again,
I don't mean to post a list of problems or anything, but all the problems I have left have a common theme and I just can figure them out.
The first one is, "Use the digits 1 to 9 to make an addition problem and answer. Use each digit only once." It is set up like this: _ _ _ + _ _ _ = _ _ _. I started coming up with different combinations to equal 7, 8, and 9 that didn't conflict which each other because I figured they were most likely to be on the bottom. When I couldn't find any that worked, I realized that you could carry a number over, meaning the bigger numbers didn't necessarily have to be on the bottom. Is there any way to figure this out other than guessing and checking every single combination of of numbers against every other combination?
The next one is, place the digits 2, 3, 4, 5, 6, 7, 8 in the boxes to obtain the (a) greatest sum and the (b) least sum. The boxes are set up as _ _ _ + _ _ _. I can guess what seem to be the biggest and smallest sums, but how do I know that I'm right? (Other than looking in the back, obviously.) Edit: I figured this one out... albeit by guessing and checking the back of the book, so I'd still like to know if there's a more concrete way, but at least I got it.
Next one is one of those cryptograms or whatever they're called. I hate these. I can't understand them for the life of me. In the following problems, each letter represents a different digit and any of the digits 0 through 9 can be used. However, both additions have the same result. What are the problems? The 2 problems given are ZZZ + KKK + LLL = RSTU and ZZZ + PPP + QQQ = RSTU. I'm really not sure about cryptograms to begin with, but 2 of them that have to have the same answer gets me even more confused. I'm pretty sure R has to be 1, and even that I can't be certain of because as I've had it explained to me, if the answer is one digit longer, that digit is 1 because it was carried, but you can carry other digits, too.
Anyway, I'm sorry to ask so many questions, but I have no idea how to solve any of these problems other than guess. I'm trying, I really am - for example, I had "Arrange the digits 1, 2, 3, 4, 5, 6, 7 such that they add up to 100" and after about 10 minutes of guess and check I figured it out, but that's all I know how to do - guess. Is there a better way?
Thank you so much for all your help, I really appreciate it!
I don't mean to post a list of problems or anything, but all the problems I have left have a common theme and I just can figure them out.
The first one is, "Use the digits 1 to 9 to make an addition problem and answer. Use each digit only once." It is set up like this: _ _ _ + _ _ _ = _ _ _. I started coming up with different combinations to equal 7, 8, and 9 that didn't conflict which each other because I figured they were most likely to be on the bottom. When I couldn't find any that worked, I realized that you could carry a number over, meaning the bigger numbers didn't necessarily have to be on the bottom. Is there any way to figure this out other than guessing and checking every single combination of of numbers against every other combination?
The next one is, place the digits 2, 3, 4, 5, 6, 7, 8 in the boxes to obtain the (a) greatest sum and the (b) least sum. The boxes are set up as _ _ _ + _ _ _. I can guess what seem to be the biggest and smallest sums, but how do I know that I'm right? (Other than looking in the back, obviously.) Edit: I figured this one out... albeit by guessing and checking the back of the book, so I'd still like to know if there's a more concrete way, but at least I got it.
Next one is one of those cryptograms or whatever they're called. I hate these. I can't understand them for the life of me. In the following problems, each letter represents a different digit and any of the digits 0 through 9 can be used. However, both additions have the same result. What are the problems? The 2 problems given are ZZZ + KKK + LLL = RSTU and ZZZ + PPP + QQQ = RSTU. I'm really not sure about cryptograms to begin with, but 2 of them that have to have the same answer gets me even more confused. I'm pretty sure R has to be 1, and even that I can't be certain of because as I've had it explained to me, if the answer is one digit longer, that digit is 1 because it was carried, but you can carry other digits, too.
Anyway, I'm sorry to ask so many questions, but I have no idea how to solve any of these problems other than guess. I'm trying, I really am - for example, I had "Arrange the digits 1, 2, 3, 4, 5, 6, 7 such that they add up to 100" and after about 10 minutes of guess and check I figured it out, but that's all I know how to do - guess. Is there a better way?
Thank you so much for all your help, I really appreciate it!