What is the key for these two operations?
L I O N
R A T
-------------
L T H L R T
O P H P L
----------------
L A P I N | O A H N R R T | R N
O P N I E L
-------------
E L T L L T
E E E T R H
-----------
E L P L
So this is structured as a multiplication stacked on top of division.
The multiplication has two partial products instead of three, suggesting that one of the digits in RAT is a 0. T=0 makes sense to have the first partial product be LION*A shifted by a digit.
With T=0 then I look at the lower difference of the division. I can split this in half: LT-EE=E and LT-RH=PL.
From LT-EE=E with T=0 then E=5 and then L=6.
Then LT-RH=PL becomes 60-RH=P6. Then H=4 and R+P=5, but we already used 4 so R and P are 2 and 3 in some order.
Going back to the sum in the product, we must have L+L end in R, with L=6 then R=2, so P=3.
Then with T=0 there is no carry into L+P=A, with P=3 and L=6 then A=9.
The main product has multiplicand beginning with a 6 and a multiplier beginning with 3. The unused digits are 1, 7 and 8, so the only option that makes sense is that O must be 1.
Back to the first difference in the division for N-I=0 then there is a borrow with N and I being consecutive. And the only available digits are 7 and 8, therefore I=7 and N=8
The decoded problem:
6 7 1 8
2 9 0
-------------
6 0 4 6 2 0
1 3 4 3 6
----------------
6 9 3 7 8 | 1 9 4 8 2 2 0 | 2 8
1 3 8 7 5 6
-------------
5 6 0 6 6 0
5 5 5 0 2 4
-----------
5 6 3 6
Key: T=0, O=1, R=2, P=3, H=4, E=5, L=6, I=7, N=8, A=9
Solution
