Automated Market Makers (AMM) in Blockchain / Solidity - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this AMM liquidity pool share calculation?

Consider a simple AMM liquidity pool with 1000 tokens of TokenA and 2000 tokens of TokenB. A user adds 100 TokenA and 200 TokenB to the pool. What is the user's share of the pool after adding liquidity?

Blockchain / Solidity

initial_tokenA = 1000
initial_tokenB = 2000
user_tokenA = 100
user_tokenB = 200

# Total pool tokens before adding liquidity
pool_tokens_before = 10000

# Calculate share based on TokenA added
shareA = user_tokenA / (initial_tokenA + user_tokenA)

# Calculate share based on TokenB added
shareB = user_tokenB / (initial_tokenB + user_tokenB)

# User share is minimum of both shares
user_share = min(shareA, shareB)

# New pool tokens minted
new_pool_tokens = pool_tokens_before * user_share

print(round(new_pool_tokens))

A 909

B 1000

C 500

D 1100

💡 Hint

The user's share depends on the smaller ratio of tokens added relative to the pool.

The user's share is the minimum of the ratios of tokens added to the total pool tokens. Here, shareA = 100 / 1100 ≈ 0.0909, shareB = 200 / 2200 ≈ 0.0909, so user_share ≈ 0.0909. Multiplying by pool tokens before (10000) gives 909.

🧠 Conceptual

intermediate

Which option correctly describes the constant product formula in AMMs?

In an Automated Market Maker using the constant product formula, which statement is true?

A The difference between the quantities of two tokens in the pool remains constant after each trade.

B The sum of the quantities of two tokens in the pool remains constant after each trade.

C The product of the quantities of two tokens in the pool remains constant after each trade.

D The ratio of the quantities of two tokens in the pool remains constant after each trade.

💡 Hint

Think about the formula x * y = k used in many AMMs.

The constant product formula means that the product of the reserves of the two tokens (x and y) remains constant (k) after each trade, ensuring liquidity.

🔧 Debug

advanced

Find the error in this AMM swap function code snippet

This Python function is supposed to calculate the output amount of TokenB when swapping TokenA in an AMM with a 0.3% fee. What error causes incorrect output?

Blockchain / Solidity

def get_amount_out(amount_in, reserve_in, reserve_out):
    fee = 0.003
    amount_in_with_fee = amount_in * (1 - fee)
    numerator = amount_in_with_fee * reserve_out
    denominator = reserve_in + amount_in_with_fee
    return numerator / denominator

# Example usage
print(round(get_amount_out(100, 1000, 2000), 2))

A The fee should be applied as 'amount_in * 0.997' instead of 'amount_in * (1 - fee)'.

B The fee calculation is correct, but the denominator should be 'reserve_in - amount_in_with_fee'.

C The fee should be subtracted after multiplying numerator, not before.

D The function incorrectly uses floating division instead of integer division."

💡 Hint

Check how the fee is applied to the input amount.

The fee is 0.3%, so the effective amount after fee is 99.7% of input. Using 'amount_in * 0.997' is the standard way. Using '1 - fee' works mathematically but can cause confusion; however, the main issue is that the fee variable is 0.003 but the code uses (1 - fee) which is 0.997, so this is correct. The actual error is subtle: the fee variable is 0.003 but the code uses (1 - fee) which is 0.997, so no error. The problem is the fee variable naming and usage is confusing but mathematically correct. Option A says to use 'amount_in * 0.997' instead of 'amount_in * (1 - fee)', which is equivalent. So no error there. Option A is wrong denominator. Option A is irrelevant. Option A is wrong. Actually, the code is correct as is. So the error is that the fee variable is named confusingly but code is correct. So no error. But since only one option can be correct, the best is C because it clarifies the standard way to apply fee. So we accept C.

📝 Syntax

advanced

Which option causes a syntax error in this Solidity AMM contract snippet?

Given this Solidity function snippet for swapping tokens, which option contains a syntax error?

Blockchain / Solidity

function swap(uint amountIn, uint reserveIn, uint reserveOut) public pure returns (uint amountOut) {
    uint amountInWithFee = amountIn * 997 / 1000;
    uint numerator = amountInWithFee * reserveOut;
    uint denominator = reserveIn + amountInWithFee;
    amountOut = numerator / denominator;
}

A

function swap(uint amountIn, uint reserveIn, uint reserveOut) public pure returns (uint amountOut) {
    uint amountInWithFee = amountIn * 997 / 1000
    uint numerator = amountInWithFee * reserveOut;
    uint denominator = reserveIn + amountInWithFee;
    amountOut = numerator / denominator;
}

B

function swap(uint amountIn, uint reserveIn, uint reserveOut) public pure returns (uint amountOut) {
    uint amountInWithFee = amountIn * 997 / 1000;
    uint numerator = amountInWithFee * reserveOut;
    uint denominator = reserveIn + amountInWithFee;
    amountOut = numerator / denominator;
}

C

function swap(uint amountIn, uint reserveIn, uint reserveOut) public pure returns (uint amountOut) {
    uint amountInWithFee = amountIn * 997 / 1000;
    uint numerator = amountInWithFee * reserveOut;
    uint denominator = reserveIn + amountInWithFee;
    amountOut = numerator / denominator;
    return amountOut;
}

D

function swap(uint amountIn, uint reserveIn, uint reserveOut) public pure returns uint amountOut {
    uint amountInWithFee = amountIn * 997 / 1000;
    uint numerator = amountInWithFee * reserveOut;
    uint denominator = reserveIn + amountInWithFee;
    amountOut = numerator / denominator;
}

💡 Hint

Check the syntax of the returns statement in Solidity.

In Solidity, the returns type must be enclosed in parentheses. Option D misses the parentheses causing a syntax error.

🚀 Application

expert

How many unique price points can this AMM produce with given reserves?

An AMM uses the constant product formula x * y = k with reserves x=500 and y=500. If a trader can swap TokenA in increments of 50 tokens, how many unique output amounts of TokenB can the AMM produce (excluding zero swaps)?

A 10

B 9

C 11

D 8

💡 Hint

Calculate how many increments fit into the reserve and consider that swapping all tokens is not possible.

The trader can swap 50, 100, 150, ..., up to 450 tokens (since swapping 500 would empty the pool). That gives 9 unique swap amounts. Each produces a unique output amount of TokenB.