Simple Maths question?

sadcrimsonrhino

New member
Joined
Feb 23, 2021
Messages
2
Hi

My first post so apologies if this is in the wrong place etc.

My son was set the following question as part of his maths work, and whilst I think the intention may simply be to brute force a solution, I was hoping to identify a more elegant way to solve this to walk through with my son and hoped someone here may be able to help.

Question:

S.NOW+
R.AIN
________
SL.EET

Where each different letter is unique.

We have worked out the first part, and deduced that S must be 1 and therefore L must be 0, but after that we have got a bit stuck. I have seen actual solutions online, however what I am after is the method that doesn't rely on brute force.

Any ideas how to solve this?
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
10,011
There is no one method to do these type problems.
Can you show us your work so we can tell you how to proceed?
 

sadcrimsonrhino

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Feb 23, 2021
Messages
2
So our first step was to establish that SL must either be in the tens or twenties, meaning S is 1 or 2.

S Plus R must have a carry over.

The largest carry over with the available numbers will only ever be 1. So carry overs will always be 1 or 0.

Therefore R must be 7 8 or 9, as R plus (the highest of 1 or 2), (plus a possible carry over of 1) must equal 10 or more.

S can't be 2 as, 2 plus R (which is 7, 8 or 9), plus a possible remainder 1 never equates to a two digit number in the twenties. Therefor S must be 1.

If S is 1, R can no longer be 7, so must be 8 or 9.

S + R + possible carry over = 1L. We know now That R is 8 or 9 and S is 1 so, 1 + (8 or 9) + (1 or 0) = 1L. From this we can establish that L can only be zero as we have already used 1 for the value of S.

...and that's where we start to get stuck. We have used 0 and 1 already, so now only have to attribute 2/3/4/5/6/7/8/9.

Hopefully the above steps make some sort of sense (and also we haven't made some logical blunder somewhere along the way).

Any ideas how to proceed from here, or are we in fact going down a rabbit hole to no effect. As stated up front keen to avoid a brute force trial and error solution if there is a better logic or formula based approach that would work.

Many thanks
Simon
 

mrmac22448

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Joined
Feb 25, 2021
Messages
4
S.NOW+ Set up S= 1
R.AIN R = 8 or 9
________ L = 0 and so forth
SL.EET


I think that you just have to logic your way through it. S has to equal 1 because when you add two digits (even with a carry), you can't get to 20. Since S is 1, R must be either 8 (with a carry) or 9. Smaller numbers won't require a carry. L has to be a 1 or a 0, and since 1 has been taken, L = 0. Like that. You may have to guess a little and check.
 
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