2026-04-08

Problem — 2026-04-08

Easy

Easycombinatorics

How many subsets of {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\} have an even number of elements? (Include the empty set.)

Enter an integer

Show solution
Pair each even-sized subset SS with S{1}S \triangle \{1\} (toggle element 11). This creates a bijection between even-sized and odd-sized subsets, so exactly half of all 26=642^6 = 64 subsets have even size: 642=32\frac{64}{2} = 32.