Conway's

Unsolved problems

1. Create a 90° stable reflector in a 50*50 box. ($50 USD - Dave Greene)
2. Create a 90° stable reflector in a 35*35 box. ($50 USD - Dave Greene)
3. Create a steerable spaceship. ($50 USD - Amos Bairn)
4. Build a replicator.
5. Make a pattern with unstoppable quadratic growth.
6. Find a glider synthesis of a c/3 spaceship.
7. Find a glider synthesis of a c/5 spaceship.
8. Engineer a pattern with spiral growth.
9. Find oscillators for the remaining periods: 19, 23, 31, 34, 38, 41, 43, 53
10. Make a more elegant stable lightspeed transceiver than my existing monstrocity.
11. Find a way to turn a lightspeed signal quickly around a corner.
12. Build a 'reflectorless rotating oscillator'.
13. Make pure-period glider guns for all remaining periods.
14. Make a stable reflector with a recovery time less than 100.
15. Find lightspeed signals of all periods.
16. Prove, or disprove by example, that every stable pattern can be constructed from gliders.
17. Prove, or disprove, that every stable pattern has a sequence of gliders that can destroy it.
18. Find a fountain oscillator of periods 7 and 9, and a superfountain of period 6.
19. Create a pattern that can absorb any single glider fired at it and return to its original state.
20. Create a stable pattern that satisfies the above conditions.
21. Make a p14 oscillator using two copies of the 7-generation TL push.
22. Produce a p36 pre-pulsar oscillator.
23. Make an object that stretches an oblique line of ants.
24. Make a transceiver for a drifter-based lightspeed signal.
25. Prove, or disprove, the existence of a pattern with a parent but no grandparent.
26. Find a way to turn a 2c/3 signal quickly around a corner.
27. Make a direct 2c/3 signal injector.
28. Make a pattern that can directly transform a drifter into a glider.
29. Disprove, or prove by example, the existence of a c/2 'stripes agar' signal.
30. Create a suitable p30 domino sparker, so that the p15 oscillator below can be made p30:
    x = 14, y = 10, rule = B3/S23
    bb3o4b3o$6obb6o$bb3o4b3o5$4bo4bo$bboob4oboo$4bo4bo!
31. Find a 2c/5 'against-the-grain' greyship.
32. Fill in the missing gaps on the status page.
33. Build a gun for the 17c/45 Caterpillar spaceship.
34. Build a stable glider-to-2c/5 ship converter.
35. Determine whether the Fermat Prime Calculator grows indefinitely.