Find numbers that name themselves
NUMBER NAME COMPETITION
The Contest Center
59 DeGarmo Hills Road
Wappingers Falls, NY 12590



We will post the names of everyone
who finds new or better solutions.




       The letters in the name of any natural number can be mapped into a sequence of numbers in a natural way by setting A=1, B=2, C=3, ..., Z=26. So ONE = (15,14,5), TWO=(20,23,15), THREE=(20,8,18,5,5), and so forth. These sequences of numbers, in turn, can be used to form arithmetic expressions. When the value of the expression equals the original number, the number is called self-referential.
       There are no numbers where the value of the letters adds up to the number. But, other expressions can equal the original number. The table below gives some examples to start off.
       The competition is to find more examples, or to improve any existing examples. You may use any number which has a standard accepted name. The American system, where ONE BILLION means 1,000,000,000 will be used. The letters of the number name must appear in order. The allowable operations are addition, subtraction, multiplication, division and exponentiation (raising a number to a power). The standard rules of mathematical precedence apply, so 1+2x3 is 7, not 9. That is, 1+2x3 is equivalent to 1+(2x3) and not (1+2)x3.
       Each entry is scored as follows: the number of letters in the name, PLUS the number of digits in the number, MINUS 1 for each plus or minus sign, MINUS 2 for each multiplication or division sign, MINUS 3 for each exponentiation, MINUS 1 for each required parenthesis. You can beat a previous solver by finding a higher-scoring expression for the same number.

Please submit your entries in the same format as the table, for example
(T+H-R+E)/E = (20+8-18+5)/5 = 3


Score Expression Found by
-2 (O-N)^E = (15-14)5 = 1 Frank Rubin
-1 (T+H-R+E)/E = (20+8-18+5)/5 = 3 Frank Rubin
-2 (-T-H+R)/E+E = (-20-8+18)/5+5 = 3 Susil Kumar Jena
-3 T/(-H+R)+E/E = 20/(-8+18)+5/5 = 3 A. Ross Eckler
-1 F-(O+U)/R = 6-(15+21)/18 = 4 Nick McGrath
2 (-F+I+V)/E = (-6+9+22)/5 = 5 Nick McGrath
0 -S-E+V-E+N = -19-5+22-5+14 = 7 A. Ross Eckler
1 -T/E+N = -20/5+14 = 10 A. Ross Eckler
3 E-L+E+V+E-N = 5-12+5+22+5-14 = 11 Nick McGrath
0 -E-L/E+V/E+N = -5-12/5+22/5+14 = 11 A. Ross Eckler
-1 -T-W+E-(L-V)×E = -20-23+5-(12-22)×5 = 12 Eckler/Rubin
3 T+H-I+R-T+E+E-N = 20+8-9+18-20+5+5-14 = 13 Paul Cleary
2 -T+H+I-R+T+E-E+N = -20+8+9-18+20+5-5+14 = 13 A. Ross Eckler
3 F+O-U+R+T-E-E-N = 6+15-21+18+20-5-5-14 = 14 A. Ross Eckler
3 F-I-F+T-E-E+N = 6-9-6+20-5-5+14 = 15 A. Ross Eckler
1 S-I+X+T×E-E×N = 19-9-24+20×5-5×14 = 16 Frank Rubin
0 S+I-X-T/(E+E)+N = 19+9-24-20/(5+5)+14 = 16 A. Ross Eckler
3 S+E-V+E+N+T-E-E-N = 19+5-22+5+14+20-5-5-14 = 17 ---
1 -E-I+G×H-T+E+E-N = -5-9+7×8-20+5+5-14 = 18 Frank Rubin
2 N+I-N-E-T/E+E+N = 14+9-14-5-20/5+5+14 = 19 A. Ross Eckler
2 N-I-N-E+T-E/E+N = 14-9-14-5+20-5/5+14 = 19 Susil Kumar Jena
3 T+W+E+N-T-Y-O+N+E = 20+23+5+14-20-25-15+14+5 = 21 Paul Cleary
2 T-W×E+N+T+Y+T+W+O = 20-23×5+14+20+25+20+23+15 = 22 Frank Rubin
3 T-W-E-N-T+Y+T-H+R+E+E = 20-23-5-14-20+25+20-8+18+5+5 = 23 Paul Cleary
2 -T-W+E-N+T+Y+T-H+R+E-E = -20-23+5-14+20+25+20-8+18+5-5 = 23 Gerald Harrison
2 T-W-E-N+T-Y+F×O-U-R = 20-23-5-14+20-25+6×15-21-18 = 24 Frank Rubin
3 T-W-E-N-T+Y+F+I+V+E = 20-23-5-14-20+25+6+9+22+5 = 25 Paul Cleary
2 T-W+E×N-T-Y+S+I-X = 20-23+5×14-20-25+19+9-24 = 26 Frank Rubin
2 T-W-E+N+T+Y+S+E+V-E×N = 20-23-5+14+20+25+19+5+22-5×14 = 27 Frank Rubin
3 T-W+E+N+T-Y+E-I-G+H+T = 20-23+5+14+20-25+5-9-7+8+20 = 28 Frank Rubin
3 T-W+E-N+T+Y-N-I+N+E = 20-23+5-14+20+25-14-9+14+5 = 29 Paul Cleary
2 T-H-I+R-T-Y-O+N×E = 20-8-9+18-20-25-15+14×5 = 31 Frank Rubin
3 T+H+I+R-T+Y-T-W+O = 20+8+9+18-20+25-20-23+15 = 32 Frank Rubin
2 T+H+I-R+T+Y+T-H-R-E×E = 20+8+9-18+20+25+20-8-18-5×5 = 33 Frank Rubin
2 T-H×I+R+T+Y+F-I+V+E = 20-8×9+18+20+25+6-9+22+5 = 35 Frank Rubin
2 -T-H+I+R+T+Y+S+E-V+E-N = -20-8+9+18+20+25+19+5-22+5-14 = 37 Gerald Harrison
2 -F+O+R-T+Y-S+I+X = -6+15+18-20+25-19+9+24 = 46 Gerald Harrison
3 O×N×E-T-H-O+U-S+A-N+D = 15×14×5-20-8-15+21-19+1-14+4 = 1000 Frank Rubin
2 (O+N-E×H+U+N+D-R)^E+D-T+H+O+U-S+A-N+D =
(15+14-5×8+21+14+4-18)^5+4-20+8+15+21-19+1-14+4 = 100,000 		Frank Rubin
2 (O+N-E×H+U+N+D-R)^E+D-T+H+O+U-S+A-N+D =
(15+14-5*8+21+14+4-18)^5+4-20+8+15+21-19+1-14+4 = 100,000 		Frank Rubin
0 (O+N-E×H+U+N+D-R)^(E+D+T+H-O+U-S-A-N-D) =
(15+14-5*8+21+14+4-18)^(5+4+20+8-15+21-19-1-14-4) = 100,000 		Nick McGrath
-1 O×N-E×H+U×N×D×R×E-D-T+H-O×U×S+A-N+D =
15×14-5×8+21×14×4×18×5-4-20+8-15×21×19+1-14+4 = 100,000 		Frank Rubin
4 (O+N-E-H-U+N+D-R-E)^(D-M+I+L-L+I-O+N) =
(15+14-5-8-21+14+4-18-5)^(4-13+9+12-12+9-15+14) = 100,000,000 		Nick McGrath
3 (O+N-E*B-I-L+L)^I*(O-N) = (15+14-5*2-9-12+12)^9*(15-14) =
1,000,000,000 		Frank Rubin
2 (-O+N+E-B*I+L+L)^I*(O-N) = (-15+14+5-2*9+12+12)^9*(15-14) =
1,000,000,000 		Susil Kumar Jena
6 (-O+N+E-T+R/I+L+L)^(I+O-N) = (-15+14+5-20+18/9+12+12)^(9+15-14) = 1,000,000,000,000 Frank Rubin
2 (O-N)*E*T*(R-I+L/L)^(I+O-N) = (15-14)*5*20*(18-9+12/12)^(9+15-14) = 1,000,000,000,000 Susil Kumar Jena
11 (O+N+E+H+U+N+D+R-E+D+T+R+I+L-L-I*O)^N =
(15+14+5+8+21+14+4+18-5+4+20+18+9+12-12-9*15)^14 =
100,000,000,000,000 		Frank Rubin
8 (O+N-E-Q-U+A-D+R+I)^(L+L-I)*(O-N) =
(15+14-5-17-21+1-4+18+9)^(12+12-9)*(15-14) = 1,000,000,000,000,000 		Susil Kumar Jena
11 (T-E-N-Q+U-A+D+R/I)^(L+L-I+O-N) =
(20-5-14-17+21-1+4+18/9)^(12+12-9+15-14) = 10,000,000,000,000,000 		Susil Kumar Jena
87 (T×(-E+N-D)-U-O-T-R-I-G)^((I+N+T-I-L-L)×(I+O-N)) =
(20×(-5+14-4)-21-15-20-18-9-7)^((9+14+20-9-12-12)×(9+15-14)) =
10100 (googol) 		Bob Ellington
298 (T×E)^(N×C+E+N+T+I+L+L+I+O+N) =
(20×5)^(14*3+5+14+20+9+12+12+9+15+14) = 10304 		Frank Rubin



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