Confession: I solved this almost exactly backwards:
I looked at the letters, guessed what the 10-letter
word or phrase would be, looked at individual products,
deduced what the 5-digit and 3-digit numbers (and hence
words) had to be, and used that to check the suspicion
I had (without having fully solved the clue) for the
8-letter word. But I'll do things forwards here :-).
Clues
House is haunted -- a phantom's turned up inside
PAD. "House" is def and PAD is a reversed substring of "haunted -- a phantom".
Trapping you and I in eternal, fiery pits? It's the greatest of Satan's tricks
RUSES. "Tricks" is def. US (you and I) is trapped in RES, which is the centres ("pits") of eteRnal and fiEry, plus S (the greatest of "Satan").
Ritual involving the drinking of blood with supernatural entities in the end roaming free, leaving behind widespread carnage
MASSACRE. "Carnage" is def. MASS (ritual involving the drinking of blood) with ACRE, which is SACRED (supernatural, kinda) with S ("entities" in the end) roaming free, and D (behind "widespread") leaving.
(Those were unusually convoluted...)
*Alphametic
P A D
_________________
R U S E S ) M A S S A C R E
M U S S C M
-----------
C J J U P R
S M E D J S
-----------
R U M P P E
A S P P C A
-----------
A E D E M
First, notice that
A-U=C, with no borrow (first subtraction, near the left), so C < A, so there's no borrow from A-C near the right of the first subtraction, so when we see S-S=J that means J=0. So the P-J=P near the right of the second subtraction means that there's no borrow from the column to its right, so R > S.
Also,
C-S and R-A both yield zero, obviously with borrows, so C = S+1 and R = A+1. So we have SC and AR in our final 10-letter word or phrase, which I am pretending I don't know yet. And the previous observation says that SC comes before AR.
Current state of play:
P A D
_________________
R U S E S ) M A S S A C R E
M U S S C M
-----------
C 0 0 U P R
S M E D 0 S
-----------
R U M P P E
A S P P C A
-----------
A E D E M
0 1 2 3 4 5 6 7 8 9
J
answer: J...SC...AR...
Now another easy observation:
we already saw that A-U=C and hence A-C=U, so the column saying as much near the right of the first subtraction doesn't have a borrow into it, so M+P=C. In particular, M,P both come between J and SC in our word-or-phrase. Also, look at the last subtraction: we have P-P=D (not J), so we must have D=9.
P A 9
_________________
R U S E S ) M A S S A C R E
M U S S C M
-----------
C 0 0 U P R
S M E 9 0 S
-----------
R U M P P E
A S P P C A
-----------
A E 9 E M
0 1 2 3 4 5 6 7 8 9
J D
answer: J...{M,P}...SC...AR...D
At this point we have
either something like JMPSCARD or something like JPMSCARD
and it's getting increasingly difficult to keep up the pretence of not knowing the final answer, but let's proceed. Look at
the second subtraction, where we have P-0=P (clearly no borrow), then U-9=M (so clearly M=U+1 and there's a borrow propagating left from there), then 0-E(-1)=U (since we have MSCARD to the right of U, we have U<=3, so E=9-U>=6. After that (borrow still propagating left) we have 0-M(-1)=R; we have JUMPSCA to the left of R so R >= 7, so M=9-R <= 2. But we also have JU to the left of M, so M >= 2. So we can lock in JUM as 012 and and hence RE=78. And remember that we know A=R-1.
P 6 9
_________________
7 1 S 8 S ) 2 6 S S 6 C 7 8
2 1 S S C 2
-----------
C 0 0 1 P 7
S 2 8 9 0 S
-----------
7 1 2 P P 8
6 S P P C 6
-----------
6 8 9 8 2
0 1 2 3 4 5 6 7 8 9
J U M A R E D
answer: JUM...P...SC...ARED
But wait,
that only leaves three spaces for P,S,C which have to come in that order, suddenly and shockingly revealing that the answer is JUMP-SCARED.
3 6 9
_________________
7 1 4 8 4 ) 2 6 4 4 6 5 7 8
2 1 4 4 5 2
-----------
5 0 0 1 3 7
4 2 8 9 0 4
-----------
7 1 2 3 3 8
6 4 3 3 5 6
-----------
6 8 9 8 2
0 1 2 3 4 5 6 7 8 9
J U M P S C A R E D
answer: JUMPSCARED
It's interesting that this was solved using only the subtractions -- we didn't need to look at the multiplications at all!
