Question

5 can you crack the code? each word relates to the theme listed above the words, but the words have been concealed by a code.
a. in the code, a new set of letters has been used in place of the normal letters. for example, in the code below, ( b ) is used in place of ( a ), ( a ) is used in place of ( n ), ( n ) is used in place of ( i ), and ( x ) is used in place of ( s ). the code is the same for all the words.
b. to break the code, fill in the o’s, i’s, n’s, and s’s. then think about things you can put on a sandwich. also watch for how often a letter appears. for example, in #6, ( m ) appears three times, so ( m ) is probably the code letter for a letter that appears often in english words.
c. when you have guessed a word, use these letters for the other words until you have cracked the code for the entire group.
theme: some things to put on your sandwich.

1. ( \frac{o}{h} \frac{n}{a} \frac{i}{n} \frac{o}{h} \frac{n}{a} \frac{s}{x} )
2. ( \frac{m}{q} \frac{u}{j} \frac{s}{x} \frac{t}{f} \frac{a}{g} \frac{r}{d} \frac{d}{i} )
3. ( \frac{m}{q} \frac{a}{g} \frac{y}{r} \frac{o}{h} \frac{n}{a} \frac{n}{a} \frac{a}{g} \frac{t}{n} \frac{s}{x} \frac{e}{m} )
4. ( \frac{p}{s} \frac{i}{n} \frac{c}{k} \frac{k}{z} \frac{l}{v} \frac{e}{m} \frac{s}{x} )
5. ( \frac{r}{z} \frac{e}{m} \frac{t}{f} \frac{c}{k} \frac{h}{u} \frac{u}{j} \frac{e}{s} )
6. ( \frac{c}{k} \frac{h}{u} \frac{e}{m} \frac{e}{m} \frac{s}{x} \frac{e}{m} )
7. ( \frac{p}{s} \frac{e}{m} \frac{a}{g} \frac{n}{a} \frac{u}{j} \frac{t}{f} quad \frac{b}{e} \frac{u}{j} \frac{t}{f} \frac{t}{f} \frac{e}{m} \frac{r}{d} )
8. ( \frac{h}{l} \frac{e}{m} \frac{h}{v} \frac{l}{v} \frac{y}{r} )
9. ( \frac{h}{l} \frac{u}{g} \frac{m}{q} )
10. ( \frac{t}{f} \frac{o}{h} \frac{m}{q} \frac{a}{g} \frac{t}{f} \frac{o}{h} \frac{c}{m} \frac{s}{x} )

Explanation:

Step1: Identify common code letters

First, note repeated code letters: $M$ appears 3x in #6, $X$ appears frequently, $H/A$ repeat in #1.

Step2: Map to common sandwich words

Start with #1: $\frac{O}{H}\frac{N}{A}\frac{I}{N}\frac{O}{H}\frac{N}{A}\frac{S}{X}$ → matches ONIONS (so $H=O$, $A=N$, $N=I$, $X=S$).

Step3: Solve #6 with repeated $M$

$\frac{C}{K}\frac{H}{U}\frac{E}{M}\frac{E}{M}\frac{S}{X}\frac{E}{M}$ → CHEESE (so $K=C$, $U=H$, $M=E$, $X=S$ confirms Step2).

Step4: Solve #7 (two words)

Left: $\frac{P}{S}\frac{E}{M}\frac{A}{G}\frac{N}{A}\frac{U}{J}\frac{T}{F}$ → PEANUT (so $S=P$, $M=E$, $G=A$, $A=N$, $J=U$, $F=T$).
Right: $\frac{B}{E}\frac{U}{J}\frac{T}{F}\frac{T}{F}\frac{E}{M}\frac{R}{D}$ → BUTTER (so $E=B$, $J=U$, $F=T$, $M=E$, $D=R$).

Step5: Solve #2

$\frac{M}{Q}\frac{U}{J}\frac{S}{X}\frac{T}{F}\frac{A}{G}\frac{R}{D}$ → MUSTARD (so $Q=M$, $J=U$, $X=S$, $F=T$, $G=A$, $D=R$).

Step6: Solve #3

$\frac{M}{Q}\frac{A}{G}\frac{Y}{R}\frac{O}{H}\frac{N}{A}\frac{N}{A}\frac{A}{G}\frac{I}{N}\frac{S}{X}\frac{E}{M}$ → MAYONNAISE (so $Q=M$, $G=A$, $R=Y$, $H=O$, $A=N$, $N=I$, $X=S$, $M=E$).

Step7: Solve #4

$\frac{P}{S}\frac{I}{N}\frac{C}{K}\frac{K}{Z}\frac{L}{V}\frac{E}{M}\frac{S}{X}$ → PICKLES (so $S=P$, $N=I$, $K=C$, $Z=K$, $V=L$, $M=E$, $X=S$).

Step8: Solve #5

$\frac{R}{Z}\frac{E}{M}\frac{T}{F}\frac{C}{K}\frac{H}{U}\frac{U}{J}\frac{E}{M}$ → RELISH (corrected: $\frac{R}{Z}\frac{E}{M}\frac{L}{V}\frac{I}{N}\frac{S}{X}\frac{H}{U}$ → no, matches RELCUUE → fix: $\frac{R}{Z}\frac{E}{M}\frac{T}{F}\frac{H}{U}\frac{O}{H}\frac{R}{D}$ → REHOUND no, correct: $\frac{R}{Z}\frac{E}{M}\frac{T}{F}\frac{C}{K}\frac{H}{U}\frac{E}{M}$ → RETCKHE = RELISH (so $Z=R$, $M=E$, $F=T$, $K=C$, $U=H$, $S=I$).

Step9: Solve #8

$\frac{H}{L}\frac{E}{M}\frac{H}{V}\frac{I}{V}\frac{Y}{R}$ → HONEY (so $L=H$, $M=E$, $V=O$, $R=Y$).

Step10: Solve #9

$\frac{H}{L}\frac{A}{G}\frac{M}{Q}$ → HAM (so $L=H$, $G=A$, $Q=M$).

Step11: Solve #10

$\frac{T}{F}\frac{O}{H}\frac{M}{Q}\frac{A}{G}\frac{T}{F}\frac{O}{H}\frac{E}{M}\frac{S}{X}$ → TOMATOES (so $F=T$, $H=O$, $Q=M$, $G=A$, $M=E$, $X=S$).

Answer:

1. ONIONS
2. MUSTARD
3. MAYONNAISE
4. PICKLES
5. RELISH
6. CHEESE
7. PEANUT; BUTTER
8. HONEY
9. HAM
10. TOMATOES