Choose the word that best defines the given phrase or idiomatic expression. The phrase is "to throw up the sponge", an idiom that originally comes from boxing.

Introduction / Context:
This idiom question examines your knowledge of the expression "to throw up the sponge". The phrase comes from the sport of boxing, where a towel or sponge would traditionally be thrown into the ring by a boxer's trainer to signal surrender. In modern English, the idiom is used more widely to mean giving up a struggle or accepting defeat in any kind of contest or effort.

Given Data / Assumptions:

The phrase is "to throw up the sponge".
We assume the figurative usage in everyday language, not only in boxing.
The correct meaning must involve stopping the fight or contest and admitting defeat.

The options include ideas of surrender, challenge, disappointment, persistence, and cheating.

Concept / Approach:
Throwing up the sponge (or towel) is a traditional signal in boxing that a fighter cannot continue. Metaphorically, it now means to give up or surrender in any difficult situation. It does not mean to become disappointed without quitting, nor does it describe offering a challenge, cheating, or fighting until the end. Therefore, the option that mentions surrendering or giving up a contest is the most accurate explanation of this idiom.

Step-by-Step Solution:
Step 1: Recall or imagine the boxing origin: the trainer throws a towel or sponge into the ring to stop the fight. Step 2: Understand the figurative meaning: to stop trying and to accept that you are not going to win. Step 3: Option A To surrender or give up a contest directly matches this idea. Step 4: Option B To offer a challenge suggests starting a fight or contest, which is the opposite of giving up. Step 5: Option C To become utterly disappointed refers to an emotional state but not necessarily to actually giving up. Step 6: Option D To maintain grit and enthusiasm until the end means to keep fighting or trying, which is the opposite of surrender. Step 7: Option E To cheat in order to win introduces dishonesty, which is unrelated to the idea of voluntarily accepting defeat.

Verification / Alternative check:
Consider a non-boxing example: "After three business failures, he finally threw up the sponge and took a regular job." This clearly means he gave up trying to run a business. If we replace the phrase with "surrendered" or "gave up the contest", the sentence still makes sense. However, replacing it with "offered a challenge" or "maintained grit until the end" would contradict the narrative of quitting. "Became utterly disappointed" might be true emotionally but would not necessarily involve stopping efforts, so it is incomplete as an explanation.

Why Other Options Are Wrong:
Option B To offer a challenge describes initiating conflict or competition, whereas the idiom is about ending one by giving up.
Option C To become utterly disappointed may often accompany giving up, but disappointment alone does not capture the clear surrender signalled by throwing up the sponge.
Option D To maintain grit and enthusiasm until the end means to persist, the direct opposite of the idiom's meaning.
Option E To cheat in order to win focuses on dishonest methods of winning and does not involve surrender at all.

Common Pitfalls:
Because some idioms refer to emotions, students sometimes confuse sadness or disappointment with actual decisions to quit. The key with "throw up the sponge" is the action of surrendering, not just feeling bad. When faced with idiom questions, always remember the original context if you know it. In this case, the boxing origin makes it easy to see that the idiom must refer to stopping the fight, not continuing or cheating.

Final Answer:
The phrase "to throw up the sponge" means to surrender or give up a contest.