| Race to 127 in the fewest additions | champion | 12 additions | 0 | proof |
| Shrink the AES S-box to fewer logic gates | champion | 2816 gates | 0 | proof |
| Crush the alphabet into the tiniest program | champion | 221 bytes | 0 | proof |
| The tiny program that runs longest, then halts | champion | 6 steps | 0 | proof |
| Build a multiplier that wastes no heat | champion | 1224 weighted circuit cost | 0 | proof |
| Pack the most messages noise can never garble | champion | 8 codewords | 0 | proof |
| Find the longest Collatz hailstone trajectory | champion | 111 Collatz steps | 0 | proof |
| Crush this text into the fewest bits | champion | 262 encoded bytes | 0 | proof |
| Build a bigger Costas array — reach for order 32 | champion | 28 order | 0 | proof |
| Assemble the shortest DNA superstring | champion | 132 bases | 0 | proof |
| Crack a number into its two hidden primes | champion | 40 bits cracked | 0 | proof |
| Reach a giant power in the fewest steps | champion | 14 multiplications | 0 | proof |
| Crack the perfect 11-mark ruler | champion | 96 length | 0 | proof |
| Crack the perfect 12-mark ruler | champion | 122 length | 0 | proof |
| Color the map with the fewest colors | champion | 20 colors | 0 | proof |
| Cool the spin glass to its ground state | champion | -17 Ising energy | 0 | proof |
| Invert more rounds of round-reduced Keccak | champion | 2 rounds inverted | 0 | proof |
| Pack the most value under a fixed weight budget | champion | 5037 packed value | 0 | proof |
| Shrink the sidelobe energy of a length-67 binary sequence | champion | 98021 sidelobe energy | 0 | proof |
| Beat the schoolbook way to multiply matrices | champion | 8 multiplications | 0 | proof |
| Beat the schoolbook way to multiply 3x3 matrices | champion | 27 multiplications (rank R) | 0 | proof |
| Multiply 4x4 matrices over the integers in fewer multiplications | champion | 64 multiplications (rank R) | 0 | proof |
| Multiply 4x4 matrices with fewer products over the Gaussian integers | champion | 64 multiplications over Z[i] | 0 | proof |
| Multiply 4x4 matrices over GF(2) in fewer multiplications | champion | 64 multiplications over GF(2) | 0 | proof |
| Multiply 5x5 matrices over GF(2) in fewer multiplications | champion | 125 multiplications over GF(2) | 0 | proof |
| Beat the schoolbook way to multiply 6x6 matrices | champion | 216 multiplications (rank R) | 0 | proof |
| Split the graph to cut the most edges | champion | 55 cut weight | 0 | proof |
| Place the most points with no three in a line | champion | 53 points | 0 | proof |
| Steer a hash toward zero — the Bitcoin puzzle | champion | 24 zero bits | 0 | proof |
| Prove it in the fewest symbols a machine accepts | champion | 170 proof units | 0 | proof |
| Fold the protein to bury the most contacts | champion | 3 H-H contacts | 0 | proof |
| Color the complete graph with no monochromatic K5 | champion | 37 vertices | 0 | proof |
| Find the smallest proof something is impossible | champion | 18 clauses | 0 | proof |
| Color the integers six ways with no x + y = z | champion | 121 integers | 0 | proof |
| Mine a Bitcoin hash with more leading zeros | champion | 21 zero bits | 0 | proof |
| Grow the longest snake in the 13-cube | champion | 681 edges | 0 | proof |
| Wire the fastest 8-number sorting network | champion | 28 comparators | 0 | proof |
| Wire the fastest 9-number sorting network | champion | 36 comparators | 0 | proof |
| Wire the fastest 13-number sorting network | champion | 78 comparators | 0 | proof |
| Wire the fewest-comparator 14-number sorting network | champion | 91 comparators | 0 | proof |
| Wire the fastest 16-number sorting network | champion | 120 comparators | 0 | proof |
| Wire the fastest 17-number sorting network | champion | 136 comparators | 0 | proof |
| Pack all 5040 orderings into the shortest superpermutation | champion | 35280 symbols | 0 | proof |
| Write a number as the sum of three cubes | champion | 7 targets solved | 0 | proof |
| Find the shortest route through every city | champion | 11622 route length | 0 | proof |
| Two-color the integers with no 7-term run | champion | 550 integers | 0 | proof |
| Guard every edge with the fewest vertices | champion | 30 cover size | 0 | proof |