Squinchy wrote:
JellyFish72 wrote:
I need help with a math problem... I can't figure it out...
Quote:
+SOME
+MORE
.SENSE
Some hints:
Try to find relationships that are "must"'s. For example, how can two digits add up to the same digit? Which digits do that?
Also, look at the first S in sense. Since there are only two rows of digits being added, the maximum value of SE is 18. (EDIT: Or 19, if you carry from the column before) What's the most likely value of S?
Errr...then, start thinking really hard (because I can't) and hope you get lucky.
G'luck!
I can think "really hard", though. And I can step you through it.
The Problem wrote:
+SOME
+MORE
.SENSE
Notice how you have E+E=E? And because it's in the one's place, nothing can carry into it. Let's try a number of things:
0+0=0 (this works)
1+1=2
2+2=4
3+3=6
4+4=8
5+5=10
6+6=12
7+7=14
8+8=16
9+9=18.
Looks to me that E must equal 0. So now we have:
The Problem wrote:
+SOM0
+MOR0
.S0NS0
I am assuming that no number can be represented by 2 letters as I continue on. As we look at S+M. We have to note that 9+9=18 and 9+8=17. Plus the optional 1 from carrying makes 19 or 18. Either way, you still have a 1 in the tens place. So S must therefore be 1.
The Problem wrote:
+1OM0
+MOR0
.10N10
Let's look at the M now. We see M+R=1 and M+1(+1 depending on carrying)=10. Doing a bit of algebra, we find that M=8 or 9 (subtracting the one from both sides and another optional one). If M=8, then R=3 because 8+3= 11 (no other single digit +8 comes out with a 1 in the ones place. I'll let you prove that yourself). If M=9, then R=2. So now we have.
The Problem wrote:
+1O80
+8O30
.10N10
Or
The Problem wrote:
+1O90
+9O20
.10N10
Either way, a 1 carries into the next column. So now you can look at the next part O+O+1=N. If M=8, we need this to carry, if M=9, we don't. Let's look at the M=8 variant first. What numbers left can we double +1 to make a two digit number (that conviently ends in a number in the ones place we also haven't used yet)?
5+5+1=11
6+6+1=13
7+7+1=15 (this could work)
9+9+1=19
We now have one set of numbers that work, but that doesn't mean we can forget about M=9 just yet and before we even go on to that, we'll check the problem.
The Problem wrote:
+1780
+8730
.10510
Yah. It works. Let's look at M=9. If M=9, then O+O+1 cannot equal a two digit number because 1+9=10 and we can't have anything carry into 1+9. The +1 comes from carrying from the 9+2. So then substituting O for numbers we haven't used yet...
3+3+1=7 (could work)
4+4+1=9
We have yet another set of answer. Let's plug this new set in.
The Problem wrote:
+1390
+9320
.10710
And it works. So we have two answers to this problem.
S=1, O=7, M=8, E=0, R=3, N=5
OR
S=1, O=3, M=9, E=0, R=2, N=7.
Hope that was helpful.
Iced - Silver [dot] Net ... now go. And maybe someday I'll actually get up something that resembles a pretty sig.