[frostybabygurl]

So my daughter came home with this homework that's just for fun, and we were all stumped, I'm wondering if anyone can help me with the correct answers.

There are 3 groups of #'s, you must use one # from each group and the total sum must be 99. You can't use any of the #s more than one time. See the groups below.

42 72 61 20 35 54 50 9
54 10 6 16 29 10 8 25 58
18 66 48 56 47 18 22
25 80 39 15 11 18 10 20 37

There should be 11 combinations. Thanks

[Unknown008]

Incidentally, there are 11 numbers in each group. I haven't found the answers yet, but it seems to me that you use all the numbers once. So, that could make things easier...

First one I got: 66, 11, 22

Hmm, nope, you can also have 66, 15, 18.

I'll see it tomorrow...

[galactus]

How about 72+18+9=99?

That's one from each group.

[ArcSine]

Yep, there are indeed 11 3-number combos summing to 99, with one number from each group, and with each number used only once. Here's another one: 10, 35, 54.

(OK, I cheated a bit: I set up the groups in a little matrix and let Excel whip through the combinations for me :cool: hey, it's the weekend... my motivation for long involved thinking plummets like a rock on Friday afternoon!)

(Word of warning: There are some combos that add to 99, but have to be rejected 'cause they use up a number that's required for a different combo. For example, Unk8's 66, 15, 18 is the good one; the 66, 11, 22 has to be rejected because the 11 and the 22 are both required elsewhere.)

[Unknown008]

Oh, I missed the part where the numbers were to be used only once... :o I shouldn't be here when it's past midnight...

[morgaine300]

Without cheating with Excel, I solved this in 11 minutes. I don't know if there's some kind of "trick" to it. I've just been doing puzzles my whole life and have done some very similar to this one, so I just know ways to go about solving these.

I like that your daughter has been given this, cause I see way too many people coming out of school without ever learning how to think about anything. Since I did puzzles even as a kid, I learned to think about stuff like this, and consequently was also not afraid of math like a lot of people are. So it'll do her good to try to solve it.

I'll tell you how I did it and let you try. Sorry, it's a little long to explain, but it's also a ridiculously simple method, assuming I explain it any good. It goes fast when you're used to doing such things, and if you get it down and get started going on it, you might get on a roll and find it not too hard.

First I put the groups into three columns. I left a couple of inches of space next to the first column for writing in.

Then the first thing I did was subtract each one in the first column from 99. (Yes, I admit to having used a calculator throughout, but doing that much arithmetic manually just annoys me and ruins the fun of the puzzle. :p Too prone to errors also.) So basically what I ended up with is a second column (in parenthesis) squeezed in there that was the total of what the other two numbers needed to be.

That is:
42 (57)
72 (27)
54 (45)

In other words, the 42 in the first set needs two numbers that add up to 57 from the second and third set to get 99. The 72 needs two numbers that add up to 27. Etc. ONce this was done I was able to completely ignore that first column, because I now knew what the second & third set numbers needed to add up to. So the first set numbers are unnecessary to finish.

In cases like this, starting at the extreme ends is easier and quicker. That is:
6 (93)
80 (19)
were the extreme high and low ends. That is, the 6 & 80 are from the first set. The number in parenthesis is still what the second and third set numbers need to add up to. The 93 and 19 were the extreme high and low.

Just to illustrate what I do next, let's take the 93. I know I need one number from each set. So if I simply go down the list in the second set and subtract it, it tells me what I need in the third set. And most of them weren't there. Like:
93 - 61 (from second set) = 32
There isn't any 32 in the third set so I skip it and move on:
93 - 20 = 72. No 72 in the third set. Moving on:
93 - 35 = 58. Ah ha! There's a 58 in the third set. So I wrote down 35/58 next to the 93, cause that combination works.
And then I kept moving on down the list. Using a calculator I can do this pretty quickly. In the end, there's only two combinations that add up to 93.

I then decided it was easier to jump to the lower end. That is, the 80 from the first column, leaving 19 that the second and third sets have to add up to. That's easy to do quickly cause only 5 numbers are even under 19 to begin with. That is, I can quickly jump down to 16 in the second set, then 10, 15, etc. And just skip all the rest. Again, I ended up with two combinations that worked to get 19.

And just went from there. I did that with every one. On the third set I did, there was only one combination. So I had the answer to that one. And one of the numbers was in another combination I already did, allowing me to eliminate one of those. So now I had two done. It didn't take long before I had others that only had one combination. (It actually took a while to eliminate one of those original "93" combinations.)

Don't forget to cross off the used numbers in the 2nd & 3rd sets once you find one that only has one possible combination.

In the end, 11 minutes total to do it manually like this.

It's not much different than puzzles I've done that are in grids. Like having say 25 numbers that have to be placed into a 5x5 grid. And each row, column and diagonal have to add up to some specific number. I work those in a similar manner. They're actually harder and could take me an hour or two to solve.

And yes, I do this for fun. ;)

[frostybabygurl]

Thanks to everyone who answered, I'm going to take the advice of the above user and see if my daughter and I can finally do this lol. I'll let you know how it goes :D

[frostybabygurl]

Thanks to Morgaine300, we took your advice about getting rid of the first group of #'s and she finished it in less than 15 minutes. Thank you again, my daughter has always struggled with math as have I and your explanation made a world of difference to her.

[morgaine300]

Wow, less than 15 minutes. I feel threatened. No, seriously, I'm very pleased that she caught on and was able to solve it so quickly! Next thing you know, she'll be gobbling up every math puzzle she can get her hands on. LOL.