Automated Market Makers (AMM) in Blockchain / Solidity - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the constant product in an AMM.

Blockchain / Solidity

constant_product = reserve_a [1] reserve_b

Drag options to blanks, or click blank then click option'

A/

B*

C-

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of multiplication.

The constant product formula multiplies the reserves of two tokens to keep the product constant.

2fill in blank

medium

Complete the code to calculate the output amount of token B given an input amount of token A.

Blockchain / Solidity

output_amount = reserve_b - (constant_product [1] (reserve_a + input_amount))

Drag options to blanks, or click blank then click option'

A/

B+

C*

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of division.

The output amount is calculated by dividing the constant product by the new reserve of token A after adding the input amount.

3fill in blank

hard

Fix the error in the code to correctly update reserves after a swap.

Blockchain / Solidity

reserve_a = reserve_a + [1]
reserve_b = reserve_b - output_amount

Drag options to blanks, or click blank then click option'

Ainput_amount

Boutput_amount

Cconstant_product

Dfee

Attempts:

3 left

💡 Hint

Common Mistakes

Adding output_amount to reserve_a instead of input_amount.

After a swap, reserve A increases by the input amount of token A.

4fill in blank

hard

Fill both blanks to calculate the fee deducted from the input amount.

Blockchain / Solidity

fee_amount = input_amount [1] fee_rate
net_input = input_amount [2] fee_amount

Drag options to blanks, or click blank then click option'

A*

B-

C+

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Adding fee instead of subtracting it.

The fee is calculated by multiplying the input amount by the fee rate, then subtracted from the input to get the net input.

5fill in blank

hard

Fill all three blanks to create a dictionary of token reserves with their updated values.

Blockchain / Solidity

updated_reserves = { '[1]': reserve_a, '[2]': reserve_b, '[3]': fee_amount }

Drag options to blanks, or click blank then click option'

AtokenA

BtokenB

Cfee

Damount

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect or inconsistent keys.

The dictionary keys represent the tokens and fee, mapping to their updated reserve values.

Practice

1. What is the main purpose of an Automated Market Maker (AMM) in blockchain?

easy

A. To enable token trading without a middleman using math formulas

B. To store user passwords securely

C. To mine new blocks in the blockchain

D. To create new tokens automatically

Solution

1. Step 1: Understand AMM's role

   AMMs allow users to trade tokens directly without needing a traditional exchange or middleman.

2. Step 2: Identify the key feature

   They use mathematical formulas and token reserves to set prices and enable swaps.

3. Final Answer:

   To enable token trading without a middleman using math formulas -> Option A

4. Quick Check:

   AMM = trading without middleman [OK]

Hint: AMMs trade tokens using formulas, no middleman needed [OK]

Common Mistakes:

• Confusing AMM with mining or token creation
• Thinking AMM stores passwords
• Assuming AMM creates tokens automatically

2. Which of the following is the correct formula used by a constant product AMM to maintain balance?

easy

A. x + y = k

B. x - y = k

C. x / y = k

D. x * y = k

Solution

1. Step 1: Recall AMM constant product formula

   AMMs use the formula where the product of token reserves remains constant.

2. Step 2: Identify the correct formula

   The formula is x * y = k, where x and y are token reserves and k is constant.

3. Final Answer:

   x * y = k -> Option D

4. Quick Check:

   Product of reserves = constant [OK]

Hint: Remember: AMM uses multiplication for constant product [OK]

Common Mistakes:

• Using addition or subtraction instead of multiplication
• Confusing division with the formula
• Mixing up variables and constants

3. Given an AMM with reserves x = 100 and y = 200, what is the new y reserve after adding 10 tokens to x and keeping k constant?

medium

A. 181.82

B. 220

C. 190

D. 200

Solution

1. Step 1: Calculate constant k

   k = x * y = 100 * 200 = 20000.

2. Step 2: Calculate new y after adding 10 to x

   New x = 100 + 10 = 110. New y = k / new x = 20000 / 110 ≈ 181.82.

3. Final Answer:

   181.82 -> Option A

4. Quick Check:

   New y = 20000 / 110 ≈ 181.82 [OK]

Hint: Divide k by new x to find new y quickly [OK]

Common Mistakes:

• Adding instead of dividing to find new y
• Using old y value without adjustment
• Forgetting to add tokens to x before calculation

4. Identify the error in this Python function that calculates output tokens from an AMM swap:

def get_output_amount(x_reserve, y_reserve, x_in):
    k = x_reserve * y_reserve
    new_x = x_reserve + x_in
    new_y = k / new_x
    return y_reserve - new_y

medium

A. The function returns new_y instead of the difference

B. The function uses addition instead of multiplication for k

C. The function does not account for swap fees

D. The function uses integer division instead of float division

Solution

1. Step 1: Review function logic

   The function calculates k correctly and finds new reserves after swap.

2. Step 2: Check for missing AMM details

   It does not include swap fees, which reduce the effective input amount.

3. Final Answer:

   The function does not account for swap fees -> Option C

4. Quick Check:

   Missing fees in calculation [OK]

Hint: Remember to subtract swap fees from input amount [OK]

Common Mistakes:

• Ignoring swap fees in calculations
• Confusing return values
• Using integer division in Python 3 (which is float by default)

5. You want to implement a function that calculates the output token amount from a swap on an AMM with a 0.3% fee. Given reserves x=500, y=1000, and input x_in=50, which code snippet correctly calculates the output amount?

hard

A. def swap_output(x, y, x_in):
fee = 0.003
x_in_with_fee = x_in + fee
k = x * y
new_x = x + x_in_with_fee
new_y = k / new_x
return y - new_y

B. def swap_output(x, y, x_in):
fee = 0.003
x_in_with_fee = x_in * (1 - fee)
k = x * y
new_x = x + x_in_with_fee
new_y = k / new_x
return y - new_y

C. def swap_output(x, y, x_in):
fee = 0.003
x_in_with_fee = x_in * fee
k = x * y
new_x = x + x_in_with_fee
new_y = k / new_x
return y - new_y

D. def swap_output(x, y, x_in):
fee = 0.003
x_in_with_fee = x_in / (1 - fee)
k = x * y
new_x = x + x_in_with_fee
new_y = k / new_x
return y - new_y

Solution

1. Step 1: Calculate effective input after fee

   The input tokens are reduced by the fee: x_in_with_fee = x_in * (1 - 0.003).

2. Step 2: Calculate new reserves and output

   Use constant product k = x * y, then new_x = x + x_in_with_fee, new_y = k / new_x, output = y - new_y.

3. Final Answer:

   Code snippet B correctly applies the fee and calculates output -> Option B

4. Quick Check:

   Subtract fee before adding input [OK]

Hint: Multiply input by (1 - fee) before calculation [OK]

Common Mistakes:

• Adding fee instead of subtracting
• Multiplying input by fee only
• Dividing input by (1 - fee) incorrectly