# New Bounties

I've now distributed 11 more bounties from the reward bounty fund. Each bounty is almost 375 bars (a little less due to transaction fees). 8 of the propositions are Ramsey Problems and 3 are 3 different (buggy) versions of the third "top 100" theorem.

No one has yet proven either of the Ramsey bounties from last week, so they seem hard enough for the moment. I choose two weakened versions of R(3,4) <= 9, namely R(3,4) <= 16 (using Power 4 for 16) and R(3,4) <= 32 (using Power 5 for 32).

TwoRamseyProp_3_4_Power_4 : TMa4Lc4AyMhSWuiBQmLra5Cex3wBXf15o16
TwoRamseyProp_3_4_Power_5 : TMQzy35yBcche2UXwdvoZVnt3dyp4LnFDNx

I expect these are much easier than proving R(3,4) <= 9 from last week, but by proving R(3,4) <= 9 should allow one to easily infer these two weaker versions. If no one proves a weaker version first, proving the strong version will allow someone to prove the two weaker version collect all three bounties.

The other Ramsey problems deal with R(4,4). The tight bounds correspond to R(4,4) > 17 and R(4,4) <= 18.

not_TwoRamseyProp_4_4_17 : TMFYWunQezDrkhpMUee7saZdayoEVM4SsbP
TwoRamseyProp_4_4_18 : TMbeXnozpPPnYPGE5hdooJdVvco3rwg45tS

In addition there are four weaker versions correspodning to R(4,4) > 8, R(4,4) > 16, R(4,4) <= 32 and R(4,4) <= 64.

not_TwoRamseyProp_4_4_Power_3 : TMb2Sy7PW4A7JxWuNHKhF1RyJi1ALA12yEn
not_TwoRamseyProp_4_4_Power_4 : TMV3LTHyCBnhXvur7GPWJBv9EbT5YUC4S8K
TwoRamseyProp_4_4_Power_5 : TMM1zbu3WmwYVsxxmcESD8kFqbfFQwTcR4f
TwoRamseyProp_4_4_Power_6 : TMJv5tmSnJSKJgVYvRKQVVMBttzVWdfnLJf

Finally, the third problem from the "top 100" list is denumerability of the rationals. There were 10 different formulations distributed with Megalodon 1.3, many of which are very similar, so I choose 3 representatives. When I chose them they all looked correct, but explaining them below I found problems with all three. I now think none of them are legitimate formulations of the third problem from the top 100 list, but I have already placed the three bounties so people can prove the buggy versions. Fortunately two of the three are close enough that solving them should quickly lead to a solution to a correct formulation.

form100_3_v3 : TMXKMYuE8hRapjyBpEa6rbp5tbDWKWiaANc