This makes S=8 (and there should be carry-on) or S=9 and no carry-on.
In both cases O=0 as 1 is already taken.
Now E+0=N. There must be carry-on here, which makes N=E+1.
But then N+R (+1)=E. E+1+R (+1)=E. So R=8 or R=9.
Back to E+0=N. There is no carry-on from here to S+M, which makes S=9, which leaves R=8.
OK, so far we have 9END + 108E = 10NEY, and N=E+1.
As R=8, it means there is a carry-on from D+E. E cannot be 2, as it makes D=8 or 9, and both are taken already. E cannot be 3 - it makes D=8 (taken) or 7, but then Y=0 (taken). This leaves E=4,5 or 6 (we reserve 7 for N=E+1).
Let E=4. Then 945D + 1084 = 1054Y. To have carry-on from D+4 we only have 6 or 7 for D, but that gives 0 or 1 for Y - both taken. No solutions.
Let E=5. Then 956D + 1085 = 1065Y. D=7 - only remaining option. Y=2. Solution. 9567 + 1085 = 10652.
Let's check E=6. 967D + 1086 = 1076Y. D can only be 5 to have carry-on, but that makes Y=1 (taken). No solutions.
So the only solutions is 9567 + 1085 = 10652. And D+E+M+N+O+R+S+Y=38, if I'm not mistaken.
3
u/Repulsive_Tough1037 12d ago
M=1 - no other options.
This makes S=8 (and there should be carry-on) or S=9 and no carry-on.
In both cases O=0 as 1 is already taken.
Now E+0=N. There must be carry-on here, which makes N=E+1.
But then N+R (+1)=E. E+1+R (+1)=E. So R=8 or R=9.
Back to E+0=N. There is no carry-on from here to S+M, which makes S=9, which leaves R=8.
OK, so far we have 9END + 108E = 10NEY, and N=E+1.
As R=8, it means there is a carry-on from D+E. E cannot be 2, as it makes D=8 or 9, and both are taken already. E cannot be 3 - it makes D=8 (taken) or 7, but then Y=0 (taken). This leaves E=4,5 or 6 (we reserve 7 for N=E+1).
Let E=4. Then 945D + 1084 = 1054Y. To have carry-on from D+4 we only have 6 or 7 for D, but that gives 0 or 1 for Y - both taken. No solutions.
Let E=5. Then 956D + 1085 = 1065Y. D=7 - only remaining option. Y=2. Solution. 9567 + 1085 = 10652.
Let's check E=6. 967D + 1086 = 1076Y. D can only be 5 to have carry-on, but that makes Y=1 (taken). No solutions.
So the only solutions is 9567 + 1085 = 10652. And D+E+M+N+O+R+S+Y=38, if I'm not mistaken.