# Decipher this puzzle

This is my riddle for you, to solve it you need to decipher the letters to digits:

   j m b k
+ n h s m
---------
n h b m t


the following rules must apply:

• each letter is a unique digit

which letter represent which digit?

• Welcome to Puzzling! This isn't a riddle - I've changed the tag to the correct one for you. – Deusovi May 22 '17 at 15:40
• Welcome to Puzzling. There are online solvers for Alphametic's. You can also add a no-computers tag the next time. – Techidiot May 22 '17 at 15:59
• This is just the well-known SEND + MORE = MONEY remapped. – M Oehm May 22 '17 at 16:21
• @MOehm Huh. So it is. It felt familiar, but I didn't spot that! – Rubio May 22 '17 at 16:27

Solution:

   9 5 6 7
+ 1 0 8 5
---------
1 0 6 5 2

That is -

$\begin{array}{rclcrcl}\text j&=&9&~~~~~~~&\text m&=&5\\ \text b&=&6 && \text k&=&7\\ \text n&=&1 && \text h&=&0\\ \text s&=&8 && \text t&=&2\\\end{array}$

Explanation:

n=1 is obvious on inspection.
h=0 is required because it can't be 1, and two digits don't allow carry+h+1>11.
b=m+1 and b+s>=9 because m+h=b and h=0 requires a carry (b cannot equal m)
j=9 is now required (it can't be 8 because b=m+1 and h=0 means no carry, so j cannot be 8).
Trial and error to fit the final digits suffices, since m appears 3 times and constrains things well.
We find with b=m+1 and neither b nor m can be 9, 0, or 1, that m=5 and the rest fall in line.

    9567
+ 1085
---------
= 10652

Explanation:

It is obvious that n is 1 because you get a carry over from the thousands to the tenths of thousands.
This makes j 8 or 9. Either one of these will make h either 1 or 0. But since 1 is taken, h = 0.

Recap:

    jmbk
+ 10sm
---------
= 10bmt

Going on:

In this case, j has to be 9 because 8 will not produce a carry over.

So now we have

    9mbk
+ 10sm
---------
= 10bmt

and the remaining digits

2,3,4,5,6,7,8.
b+s is at least 10 (I would say at least 11 since m cannot be 1) and b is m+1.

Stabbing blindly.

b = 8, would make m = 7

    978k
+ 10s7
---------
= 1087t

Doesn't work because s would have to be 8 or 9 which are taken.

Trying the same for b=7 leads to a wrong result also.

Now:

Trying b=6.

    956k
+ 10sm
---------
= 1065t

This leads to s = 8.
Trying b=6.
    956k
+ 1085
---------
= 1065t

and the remaining digits are 2,3,4,7. Trying the different combinations we get k=7, t = 2.

It is:

B=6 H=0 J=9 K=7 M=5 N=1 S=8 T=2

9567
+ 1085

10652

• Beat you by 11 minutes ;) Good job though! – Rubio May 22 '17 at 16:14
• @Rubio Well, appreciate your effort – CR241 May 22 '17 at 16:39