Functions (solution)
by Kai Huang
The solver needs to figure out what each function does, and then evaluate the final long expression to get the answer.
The functions always take English words as inputs and always output English words as well. Non-words are never allowed during the computations. Sometimes, a function has more than one valid output based on its definition, in which case the solver must choose the appropriate output based on the surrounding context. The functions are as follows:
| Function | Summary name | Description |
|---|---|---|
| a(x) | shiftWrap | Positionally shifts the letters of x by some amount to make a different word (letters shifted off one side are wrapped around to the other side). |
| b(x) | takeEveryOther | Takes either the odd- or even-position letters of x to form a word. |
| c(x) | getNext | Gets the next item after x in some common sequence. |
| d(x) | reverse | Reverses the letters of x to form a word. |
| e(x, y) | concatenate | Concatenates x and y into a word xy. |
| f(x) | getHomophone | Gets a homophone of x. |
| g(x) | changeGender | Gets an opposite-gender version of x. |
| h(x) | rotate | Visually rotates x 180 degrees to form a word. |
| i(x) | shiftCaesar | Caesar-shifts x into a different word. |
| j(x, y) | getLinkWord | Gets a word w such that “x w” and “w y” are both common terms. |
| k(x) | getPartner | Gets a word w that is commonly associated with x in a phrase using “and”, such as “w and x”, “the w and the x”, or “an x and a w”. |
| l(x) | getBritish | Gets a British equivalent of the American word x. |
| m(x, y) | insert | Inserts x into y somewhere such that the resulting string is a word. |
| n(x) | getAntonym | Gets an antonym of x. |
Here are the computations for the clue equations.
| ATE | = a(b(c(d(ATE)))) = shiftWrap(takeEveryOther(getNext(reverse(ATE)))) = shiftWrap(takeEveryOther(getNext(ETA))) = shiftWrap(takeEveryOther(THETA)) = shiftWrap(TEA) = ATE |
| BOREDOM | = e(f(g(h(MOS))), i(PAY)) = concatenate(getHomophone(changeGender(rotate(MOS))), shiftCaesar(PAY)) = concatenate(getHomophone(changeGender(SOW)), DOM) = concatenate(getHomophone(BOAR), DOM) = concatenate(BORE, DOM) = BOREDOM |
| BOWL | = j(k(l(FRIES)), a(MEGA)) = getLinkWord(getPartner(getBritish(FRIES)), shiftWrap(MEGA)) = getLinkWord(getPartner(CHIPS), GAME) = getLinkWord(FISH, GAME) = BOWL |
| ITEM | = a(m(b(l(ELEVATOR)), j(BEATS, TOO))) = shiftWrap(insert(takeEveryOther(getBritish(ELEVATOR)), getLinkWord(BEATS, TOO))) = shiftWrap(insert(takeEveryOther(LIFT), ME)) = shiftWrap(insert(IT, ME)) = shiftWrap(MITE) = ITEM |
| LOSE | = n(h(d(i(SOT)))) = getAntonym(rotate(reverse(shiftCaesar(SOT)))) = getAntonym(rotate(reverse(MIN))) = getAntonym(rotate(NIM)) = getAntonym(WIN) = LOSE |
| NOM | = h(f(c(j(GROUND, m(IT, GRAVY))))) = rotate(getHomophone(getNext(getLinkWord(GROUND, insert(IT, GRAVY))))) = rotate(getHomophone(getNext(getLinkWord(GROUND, GRAVITY)))) = rotate(getHomophone(getNext(ZERO))) = rotate(getHomophone(ONE)) = rotate(WON) = NOM |
| PETROL | = l(b(e(GO, i(n(BREAK))))) = getBritish(takeEveryOther(concatenate(GO, shiftCaesar(getAntonym(BREAK))))) = getBritish(takeEveryOther(concatenate(GO, shiftCaesar(FIX)))) = getBritish(takeEveryOther(concatenate(GO, ADS))) = getBritish(takeEveryOther(GOADS)) = getBritish(GAS) = PETROL |
| PICKS | = f(b(g(k(PAUPER)))) = getHomophone(takeEveryOther(changeGender(getPartner(PAUPER)))) = getHomophone(takeEveryOther(changeGender(PRINCE))) = getHomophone(takeEveryOther(PRINCESS)) = getHomophone(PICS) = PICKS |
Finally, here’s the computation for the answer expression, broken into multiple parts for easier reading.
| <part1> | = i(l(c(f(i(d(b(m(b(k(NAVY)), PREP))))))))
= shiftCaesar(getBritish(getNext(getHomophone(shiftCaesar(reverse(takeEveryOther(
= shiftCaesar(getBritish(getNext(getHomophone(shiftCaesar(reverse(takeEveryOther(
= shiftCaesar(getBritish(getNext(getHomophone(shiftCaesar(reverse(takeEveryOther( = shiftCaesar(getBritish(getNext(getHomophone(shiftCaesar(reverse(takeEveryOther(PREAMP))))))) = shiftCaesar(getBritish(getNext(getHomophone(shiftCaesar(reverse(RAP)))))) = shiftCaesar(getBritish(getNext(getHomophone(shiftCaesar(PAR))))) = shiftCaesar(getBritish(getNext(getHomophone(WHY)))) = shiftCaesar(getBritish(getNext(WYE))) = shiftCaesar(getBritish(ZEE)) = shiftCaesar(ZED) = PUT |
| <part2> | = n(a(d(g(OGRESS)))) = getAntonym(shiftWrap(reverse(changeGender(OGRESS)))) = getAntonym(shiftWrap(reverse(OGRE))) = getAntonym(shiftWrap(ERGO)) = getAntonym(GOER) = COMER |
| <part3> | = i(a(g(h(i(g(b(e(c(b(d(MOOD))), k(LEG)))))))))
= shiftCaesar(shiftWrap(changeGender(rotate(shiftCaesar(changeGender(
= shiftCaesar(shiftWrap(changeGender(rotate(shiftCaesar(changeGender(
= shiftCaesar(shiftWrap(changeGender(rotate(shiftCaesar(changeGender(
= shiftCaesar(shiftWrap(changeGender(rotate(shiftCaesar(changeGender(
= shiftCaesar(shiftWrap(changeGender(rotate(shiftCaesar(changeGender(
= shiftCaesar(shiftWrap(changeGender(rotate(shiftCaesar(changeGender( = shiftCaesar(shiftWrap(changeGender(rotate(shiftCaesar(changeGender(RAM)))))) = shiftCaesar(shiftWrap(changeGender(rotate(shiftCaesar(EWE))))) = shiftCaesar(shiftWrap(changeGender(rotate(WOW)))) = shiftCaesar(shiftWrap(changeGender(MOM))) = shiftCaesar(shiftWrap(DAD)) = shiftCaesar(ADD) = ILL |
| <part4> | = b(m(n(f(PROS)), a(SIN))) = takeEveryOther(insert(getAntonym(getHomophone(PROS)), shiftWrap(SIN))) = takeEveryOther(insert(getAntonym(PROSE), INS)) = takeEveryOther(insert(VERSE, INS)) = takeEveryOther(INVERSES) = NESS |
| <answer> | = j(m(<part1>, <part2>), e(<part3>, <part4>)) = getLinkWord(insert(<part1>, <part2>), concatenate(<part3>, <part4>)) = getLinkWord(insert(PUT, COMER), concatenate(ILL, NESS)) = getLinkWord(COMPUTER, ILLNESS) = TERMINAL |
The answer is TERMINAL.