Coding Grandmaster · project 15 of 46 · premium, free for now

XOR magic

Swap a and b with three XOR lines (no temporary variable), and write lonely(numbers) that returns the number that appears only once by XOR-ing everything together.

Learn

XOR (^) is 1 when the two bits differ. It has two lovely properties: x ^ x is 0, and x ^ 0 is x. So XOR-ing a number twice cancels it, which gives a way to swap without a spare variable, and a way to find the one number in a list that appears once when all others appear twice, because the pairs cancel.

Your task

Swap a and b with three XOR lines (no temporary variable), and write lonely(numbers) that returns the number that appears only once by XOR-ing everything together.

Stretch challenge

What if two numbers appear once? Think about splitting the list by one differing bit.

← One-line bit tricks Set, clear and toggle →

Python

Press Run to see what your program prints.

Keep going in Coding Grandmaster

Seeing the bits

Print each of 5, 12 and 255 as 8 binary digits, and write count_ones(n) that counts the 1 bits using & and >>.

Start →14

One-line bit tricks

Write is_power_of_two(n) using n & (n - 1), is_odd(n) using n & 1, and print the powers of two up to 200 using a list comprehension.

Start →16

Set, clear and toggle

Write set_bit(n, i), clear_bit(n, i), toggle_bit(n, i) and test_bit(n, i) (True or False) using shifts and bitwise operators.

Start →17

Every subset

Write subsets(items) returning a list of every subset as a list, in the order of the counter 0 to 2^n − 1, using bit tests. Print how many subsets four items have, and the subsets of two items.

Start →18

Permission flags

With READ = 4, WRITE = 2 and EXEC = 1, write grant(perms, flag), revoke(perms, flag), has(perms, flag) and describe(perms) which returns text like r-x (r, w and x, or - for a missing one).

Start →

Practise the idea

🔌 Play Logic Gate Challenge

Predict the output of AND, OR, XOR, NAND and NOR gates from their inputs.

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FAQ

XOR magic: common questions

I am stuck. What can I do?

Press Hint for a nudge, read the message next to each goal, and compare your code with the lesson text. If you still need it, Show answer reveals a model solution. Try to type it yourself rather than copy it.

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