change log for P1243426 (close)

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2021-08-0612:51:15A.Buchanan P1243426 problems cplus  update
2021-08-0612:51:15A.Buchanan P1243426 problems cpluscomm  update Jacobi v.0.6 
2021-08-0612:47:28A.Buchanan P1243426 problems stip  updateBP in 10 Wieviele Lösungen? KBP Wieviele Lösungen? 
2021-08-0612:12:07A.Buchanan P1243426 problems solution  update1. b3 a5 2. La3 b5 3. Lb4 c5 4. Sa3 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Dd2 cxb4# is one example 1. b3 a5 2. La3 b5 3. Lb4 c5 4. Sa3 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Db2 cxb4# is one example 
2021-08-0612:11:52A.Buchanan P1243426 problems solution  update1. b3 a5 2. La3 b5 3. Lb4 c5 4. Sa3 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Qd2 cxb4# is one example 1. b3 a5 2. La3 b5 3. Lb4 c5 4. Sa3 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Dd2 cxb4# is one example 
2021-08-0612:11:32A.Buchanan P1243426 problems solution  update1. b3 a5 2. La3 b5 3. Lb4 c5 4. Sa6 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Qd2 cxb4# is one example 1. b3 a5 2. La3 b5 3. Lb4 c5 4. Sa3 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Qd2 cxb4# is one example 
2021-08-0612:11:16A.Buchanan P1243426 problems solution  update1. b6 a5 2. La3 b5 3. Lb4 c5 4. Sa6 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Qd2 cxb4# is one example 1. b3 a5 2. La3 b5 3. Lb4 c5 4. Sa6 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Qd2 cxb4# is one example 
2021-08-0612:02:14A.Buchanan P1243426 problems stip  updateBP in 10.0 How many solutions? BP in 10 Wieviele Lösungen? 
2021-08-0612:01:19A.Buchanan P1243426 problems stip  updateKBP How many solutions? BP in 10.0 How many solutions? 
2021-08-0611:59:53A.Buchanan P1243426 problems solution  update1. b6 a5 2. La3 b5 3. Lb4 c5 4. Sa6 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Qd2 cxb4# 1. b6 a5 2. La3 b5 3. Lb4 c5 4. Sa6 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Qd2 cxb4# is one example 
2021-08-0611:59:40A.Buchanan P1243426 problems solution  updateE.g. 1. b6 a5 2. La3 b5 3. Lb4 c5 4. Sa6 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Qd2 cxb4# 1. b6 a5 2. La3 b5 3. Lb4 c5 4. Sa6 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Qd2 cxb4# 
2021-08-0611:59:22A.Buchanan P1243426 problems stip  updateSPG How many solutions? KBP How many solutions? 
2021-08-0611:58:58A.Buchanan P1243426 problems stip  updateHow many shortest proof games? SPG How many solutions? 
2021-08-0611:58:24A.Buchanan P1243426 problems stip  updateHow many shortest games? How many shortest proof games? 
2021-08-0611:57:54A.Buchanan P1243426 problems solution  update E.g. 1. b6 a5 2. La3 b5 3. Lb4 c5 4. Sa6 e5 5. Db1 Ta7 6. Kd1 La6 7. Kc1 Db6 8. Kb2 Ke7 9. Kc3 e4 10. Qd2 cxb4# 
2021-08-0611:56:29A.Buchanan P1243426 problems soltxt  updateEuler number, E_n, defined by generating function: sec(x) + tan(x) = Sum(n=0...infinity) E_n (x^n/n!) Here E_9 = 7,936. Black has just played cxLb5#. White moves are 1. b6 2. La3 3. Lb4 4. Sa6 5. Db1 6. Kd1 7. Kc1 8. Kb2 9. Kc3 10. Qd2. So from W2, wLc was potentially checking e7, unless blocked by sBc5. This fact allows us to complete the zigzag ordering of first 9 Bl moves Ta7 > a5 < La6 > b5 < Db6 > c5 < Ke7 > e5 < e4. There are E_9 possible orderings of these 9 moves, where the Euler number, E_n, is defined by generating function: sec(x) + tan(x) = Sum(n=0...infinity) E_n (x^n/n!). Here E_9 = 7,936  
2019-11-1113:52:22A.Buchanan Retro refgen   add  
2012-09-052:23:43A.Buchanan 1 The Electronic Journal of Combinatorics vol.11(2) 2004 refsrc   remove  
2012-09-052:20:49A.Buchanan 1 The Electronic Journal of Combinatorics vol.11(2) 2004 refsrc   add  
2012-09-052:20:05A.Buchanan 1 The Electronic Journal of Combinatorics vol.11(2) 2004 refsrc   add  
2012-09-0420:03:44A.Buchanan P1243426 problems soltxt  updateEuler number, E_n, defined by generating function: sec(x) + tan(x) = Sum(n=0...infinity) E_n (x^n/n!) Here E_9 = 7936. Euler number, E_n, defined by generating function: sec(x) + tan(x) = Sum(n=0...infinity) E_n (x^n/n!) Here E_9 = 7,936. 
2012-09-0419:52:55A.Buchanan Path enumeration (Euler) refkey addition  update Euler 
2012-06-3014:50:04A.Buchanan Non-Unique Proof Game refkey   add  
2012-06-3014:48:29A.Buchanan Path enumeration refkey   add  
2012-06-305:35:04A.Buchanan P1243426 problems soltxt  update Euler number, E_n, defined by generating function: sec(x) + tan(x) = Sum(n=0...infinity) E_n (x^n/n!) Here E_9 = 7936. 
2012-06-305:26:50A.Buchanan wKc3 wDb2 wTh1a1 wLf1 wSg1a3 wBh2g2f2e2d2c2a2b3 sKe7 sDb6 sTa7h8 sLa6f8 sSg8b8 sBe4b4b5a5h7g7f7d7 position piecesb  update15  16  
2012-06-305:26:50A.Buchanan wKc3 wDb2 wTh1a1 wLf1 wSg1a3 wBh2g2f2e2d2c2a2b3 sKe7 sDb6 sTa7h8 sLa6f8 sSg8b8 sBe4b4b5a5h7g7f7d7 position piecesw  update16  15  
2012-06-305:26:50A.Buchanan wKc3 wDb2 wTh1a1 wLf1 wSg1a3 wBh2g2f2e2d2c2a2b3 sKe7 sDb6 sTa7h8 sLa6f8 sSg8b8 sBe4b4b5a5h7g7f7d7 position position  updates lstt bBbbbld bb b b SBK BDBBBBBBT LST  s lstt bkbbbld bb b b SBK BDBBBBBBT LST 
2012-06-305:25:57A.Buchanan P1243426 problems comment  update2004 N. D. Elkies, New Directions in Enumerative Chess Problems, The Electronic Journal of Combinatorics, vol. 11(2), 2004. Problem 1 original: N.D.Elkies, New Directions in Enumerative Chess Problems, The Electronic Journal of Combinatorics, vol. 11(2), 2004. 
2012-06-2920:27:48A.Buchanan wKc3 wDb2 wTh1a1 wLf1 wSg1a3 wBh2g2f2e2d2c2a2b3e7 sDb6 sTa7h8 sLa6f8 sSg8b8 sBe4b4b5a5h7g7f7d7 position piecesb  update16  15  
2012-06-2920:27:48A.Buchanan wKc3 wDb2 wTh1a1 wLf1 wSg1a3 wBh2g2f2e2d2c2a2b3e7 sDb6 sTa7h8 sLa6f8 sSg8b8 sBe4b4b5a5h7g7f7d7 position piecesw  update7  16  
2012-06-2920:27:48A.Buchanan wKc3 wDb2 wTh1a1 wLf1 wSg1a3 wBh2g2f2e2d2c2a2b3e7 sDb6 sTa7h8 sLa6f8 sSg8b8 sBe4b4b5a5h7g7f7d7 position position  updates lstt bkbbbld bb b b S K D T LST  s lstt bBbbbld bb b b SBK BDBBBBBBT LST 
2012-06-2920:25:38A.Buchanan Mathematics refgen   add  
2012-06-2920:25:38A.Buchanan wKc3 wDb2 wTh1a1 wLf1 wSg1a3 sKe7 sDb6 sTa7h8 sLa6f8 sSg8b8 sBe4b4b5a5h7g7f7d7 position   add  
2012-06-2920:25:37A.Buchanan Noam D. Elkies refaut   add  
2012-06-2920:25:37A.Buchanan P1243426 problems fcooked  update 
2012-06-2920:25:37A.Buchanan P1243426 problems cplus  update 
2012-06-2920:25:37A.Buchanan P1243426 problems comment  update 2004 N. D. Elkies, New Directions in Enumerative Chess Problems, The Electronic Journal of Combinatorics, vol. 11(2), 2004. 
2012-06-2920:25:37A.Buchanan P1243426 problems stip  update How many shortest games? 
2012-06-2920:25:37A.Buchanan P1243426 problems   add