MathJaxMap['math_1'] = '3a1+a2+3a3+a4+3a5+a6+3a7+a8+3a9+a10+3a11+a12';
MathJaxMap['math_2'] = '3 ⋅ 0 + 5 + 3 ⋅ 8 + 0 + 3 ⋅ 0 + 0 + 3 ⋅ 0 + 0 + 3 ⋅ 1 + 2 + 3 ⋅ 7 + 7 = 62';
MathJaxMap['math_3'] = 'a1+3a2+a3+3a4+a5+3a6+a7+3a8+a9+3a10+a11+3a12+a13';
MathJaxMap['math_4'] = '1+3⋅x+4+3⋅0+2+3⋅0+2+3⋅2+0+3⋅2+0+3⋅3+4=3x+32';
MathJaxMap['math_5'] = '7a1+3a2+9a3+7a4+7a5+9a6+7a7+3a8';
MathJaxMap['math_6'] = '7⋅0+3⋅6+9⋅2+7⋅0+3⋅0+9⋅0+7⋅0+3⋅1=39';
MathJaxMap['math_7'] = '2⋅4+1+2⋅2+8+2⋅0+0+2⋅1+2+2⋅3+4+2⋅5+6+2⋅7+8+2⋅9+3+0=94';
MathJaxMap['math_8'] = '(10⋅a1+9⋅a2+8⋅a3+⋯+a10)−(10⋅a1+9⋅a′2+8⋅a3+⋯+a10)=9⋅(a2−a′2)';
MathJaxMap['math_9'] = '(10a1+9a2+8a3+⋯+a10)−(10a2+9a1+8a3+⋯+a10)';
MathJaxMap['math_10'] = '3⋅0+5+3⋅8+0+3⋅0+0+3⋅0+0+3⋅1+2+3⋅7+7=62';
MathJaxMap['math_11'] = '8+0+3+2+1+0+4+2+1=21';
MathJaxMap['math_12'] = 'a, e, i, o, u, y→0l→4b, f, p, v→1m, n→5b, f, j, k, q, s, x, z→2r→6d, t→3';
MathJaxMap['math_13'] = '1+7+6+2+0+2+0+2+8+9+5+2=42';
MathJaxMap['math_14'] = 'a';
MathJaxMap['math_15'] = 'b';
MathJaxMap['math_16'] = 'q';
MathJaxMap['math_17'] = 'r';
MathJaxMap['math_18'] = 'a=bq+r';
MathJaxMap['math_19'] = 'r';
MathJaxMap['math_20'] = 'b';
MathJaxMap['math_21'] = 'q';
MathJaxMap['math_22'] = 'r';
MathJaxMap['math_23'] = '42=9×4+6';
MathJaxMap['math_24'] = '3+8+7+5+0+5+0+5+5+=38';
MathJaxMap['math_25'] = '38+7';
MathJaxMap['math_26'] = '540047 = 7 × 77149 + 4';
MathJaxMap['math_27'] = '450047 = 7 × 64292 + 3';
MathJaxMap['math_28'] = 'a';
MathJaxMap['math_29'] = 'b';
MathJaxMap['math_30'] = 'a÷b';
MathJaxMap['math_31'] = 'q';
MathJaxMap['math_32'] = 'r=a−bq';
MathJaxMap['math_33'] = '123÷7';
MathJaxMap['math_34'] = '123−(7×17)=4';
MathJaxMap['math_35'] = 'a1a2a3a4a5a6a7a8a9a10a11a12';
MathJaxMap['math_36'] = 'a1a2a3a4a5a6a7a8a9a10a11a12a13';
MathJaxMap['math_37'] = '1ai=ai';
MathJaxMap['math_38'] = 'x';
MathJaxMap['math_39'] = '3x+32';
MathJaxMap['math_40'] = '2x+32';
MathJaxMap['math_41'] = 'x=4';
MathJaxMap['math_42'] = 'x=9';
MathJaxMap['math_43'] = 'a1a2 ⋯ a8';
MathJaxMap['math_44'] = 'a9';
MathJaxMap['math_45'] = 'a9';
MathJaxMap['math_46'] = '⋯abc⋯→⋯cba⋯';
MathJaxMap['math_47'] = '3⋅2+4+3⋅1=13';
MathJaxMap['math_48'] = '3⋅1+4+3⋅2=13';
MathJaxMap['math_49'] = '7⋅2+3⋅4+9⋅1=35';
MathJaxMap['math_50'] = '7⋅1+3⋅4+9⋅2=37';
MathJaxMap['math_51'] = '71a3a4⋯a9';
MathJaxMap['math_52'] = '71a3a4⋯a9';
MathJaxMap['math_53'] = 'a1a2a3a4a5a6a7a8a9a10a11a12a13a14a15';
MathJaxMap['math_54'] = 'T';
MathJaxMap['math_55'] = 'a16';
MathJaxMap['math_56'] = '2a1+a2+2a3+a4+2a5+a6';
MathJaxMap['math_57'] = '2⋅3+1+2⋅2+5+2⋅6+0+2⋅0+1+2⋅9+6+2⋅4+3+2⋅0';
MathJaxMap['math_58'] = '68+2=70';
MathJaxMap['math_59'] = '1,2,1,2,…,1,2';
MathJaxMap['math_60'] = '2,1,2,1,…,2,1';
MathJaxMap['math_61'] = 'a1a2⋯a10';
MathJaxMap['math_62'] = '10a1+9a2+8a3+7a4+6a5+5a6+4a7+3a8+2a9+a10';
MathJaxMap['math_63'] = '10⋅1+9⋅4+8⋅6+7⋅4+6⋅1+5⋅2+4⋅4+3⋅7+2⋅3+6=187';
MathJaxMap['math_64'] = '187=11⋅17';
MathJaxMap['math_65'] = 'a1a2a3a4a5a6a7a8a9a10';
MathJaxMap['math_66'] = 'a1a′2a3a4a5a6a7a8a9a10';
MathJaxMap['math_67'] = 'a′2≠a2';
MathJaxMap['math_68'] = '10⋅a1+9⋅a′2+8⋅a3+7⋅a4+6⋅a5+5⋅a6+4⋅a7+3⋅a8+2⋅a9+a10';
MathJaxMap['math_69'] = '10a1+9a2+8a3+7a4+6a5+5a6+4a7+3a8+2a9+a10';
MathJaxMap['math_70'] = '10a1+9a′2+8a3+7a4+6a5+5a6+4a7+3a8+2a9+a10';
MathJaxMap['math_71'] = 'a2';
MathJaxMap['math_72'] = 'a′2';
MathJaxMap['math_73'] = '±1,…,±9';
MathJaxMap['math_74'] = '9⋅(a2−a′2)';
MathJaxMap['math_75'] = '±9,±18±27,±36,±45,±54,±63,±72,±81';
MathJaxMap['math_76'] = '9⋅4=36';
MathJaxMap['math_77'] = '9⋅2=18';
MathJaxMap['math_78'] = '176−18=158';
MathJaxMap['math_79'] = 'a1a2a3⋯a10';
MathJaxMap['math_80'] = 'a1a2a3⋯a10';
MathJaxMap['math_81'] = 'a1−a2';
MathJaxMap['math_82'] = 'a1−a2=0';
MathJaxMap['math_83'] = 'a1=a2';
MathJaxMap['math_84'] = '9⋅4+8⋅2=52';
MathJaxMap['math_85'] = '9⋅2+8⋅4=50';
MathJaxMap['math_86'] = '176−2=174';
MathJaxMap['math_87'] = 'a';
MathJaxMap['math_88'] = '10⋅1+9⋅4+8⋅6+7⋅4+6⋅1+5⋅4+4⋅5+3⋅1+2⋅3+a=177+a';
MathJaxMap['math_89'] = 'a=10';
MathJaxMap['math_90'] = 'X';
MathJaxMap['math_91'] = 'X';
MathJaxMap['math_92'] = 'X';
MathJaxMap['math_93'] = '1,3,1,3,…,1,3,1';
MathJaxMap['math_94'] = '⋯abc⋯→⋯cba⋯';
MathJaxMap['math_95'] = '115856=8912×13';
MathJaxMap['math_96'] = '115856→115658';
MathJaxMap['math_97'] = 'anan−1⋯ai⋯a0';
MathJaxMap['math_98'] = 'anan−1⋯a′i⋯a0';
MathJaxMap['math_99'] = 'a′i≠ai';
MathJaxMap['math_100'] = 'anan−1⋯a′i⋯a0';
MathJaxMap['math_101'] = 'anan−1⋯ai⋯a0';
MathJaxMap['math_102'] = 'anan−1⋯a′i⋯a0';
MathJaxMap['math_103'] = '(anan−1⋯a′i⋯a0)−(anan−1⋯a′i⋯a0)=(ai−a′i)10i';
MathJaxMap['math_104'] = 'ai≠a′i';
MathJaxMap['math_105'] = 'ai';
MathJaxMap['math_106'] = 'ai−1';
MathJaxMap['math_107'] = '9(ai−ai−1)10i−1';
MathJaxMap['math_108'] = 'ai=ai−1';
MathJaxMap['math_109'] = '⋯aiai−1ai−2⋯→⋯ai−2ai−1ai⋯';
MathJaxMap['math_110'] = '99(ai−ai−2)10i−2';
MathJaxMap['math_111'] = 'ai=ai−2';
MathJaxMap['math_112'] = 'a1a2⋯a15a16';
MathJaxMap['math_113'] = '8⋅a1+7⋅a2+⋯+3⋅a15+2⋅a16';
MathJaxMap['math_114'] = 'a1a2a3a4a5a6a7a8a9a10a11a12';
MathJaxMap['math_115'] = '3a1+a2+3a3+a4+3a5+a6+3a7+a8+3a9+a10+3a11+a12';
MathJaxMap['math_116'] = 'a1a2a3a4a5a6a7a8a9a10a11a12a13';
MathJaxMap['math_117'] = 'a1+3a2+a3+3a4+a5+3a6+a7+3a8+a9+3a10+a11+3a12+a13';
MathJaxMap['math_118'] = 'a1a2a3a4a5a6a7a8';
MathJaxMap['math_119'] = 'a9';
MathJaxMap['math_120'] = '7a1+3a2+9a3+7a4+3a5+9a6+7a7+3a8';
MathJaxMap['math_121'] = 'a1a2a3a4a5a6a7a8a9a10a11a12a13a14a15';
MathJaxMap['math_122'] = 'T';
MathJaxMap['math_123'] = 'a16';
MathJaxMap['math_124'] = '2a1+a2+2a3+a4+2a5+a6+2a7+a8+2a9+a10+2a11+a12+2a13+a14';
MathJaxMap['math_124_2'] = '+2a15+T+a16';
MathJaxMap['math_125'] = 'a1a2⋯a10';
MathJaxMap['math_126'] = '10a1+9a2+8a3+7a4+6a5+5a6+4a7+3a8+2a9+a10';
MathJaxMap['math_127'] = 'a10';
MathJaxMap['math_128'] = 'X';
MathJaxMap['math_129'] = 'C';
MathJaxMap['math_130'] = 'a1a2⋯a9';
MathJaxMap['math_131'] = 'a1+a2+⋯+a9+C';
MathJaxMap['math_132'] = '21+9=30';
MathJaxMap['math_133'] = 'a';
MathJaxMap['math_134'] = 'e';
MathJaxMap['math_135'] = 'i';
MathJaxMap['math_136'] = 'o';
MathJaxMap['math_137'] = 'u';
MathJaxMap['math_138'] = 'y';
MathJaxMap['math_139'] = '4−0292 (292=9⋅31+13)';
MathJaxMap['math_140'] = '71a3a4⋯a8';
MathJaxMap['math_141'] = '17a3a4⋯a8, a9';
MathJaxMap['math_142'] = '17a2a3⋯a8';
MathJaxMap['math_143'] = '19a3a4⋯a107';
MathJaxMap['math_144'] = '7Xa3a4⋯a107';
MathJaxMap['math_145'] = 'X';
MathJaxMap['math_146'] = 'a1a2⋯a11';
MathJaxMap['math_147'] = 'a1a2⋯a10−a11';
MathJaxMap['math_148'] = 'X';
MathJaxMap['math_149'] = 'X';
MathJaxMap['math_150'] = 'X';
MathJaxMap['math_151'] = 'a1a2⋯ai⋯an→a1a2⋯ai'⋯an';
MathJaxMap['math_152'] = 'a1a2⋯aiai+1⋯an→a1a2⋯ai+1ai⋯an';
MathJaxMap['math_153'] = 'a1a2⋯aiai+1ai+2⋯an→a1a2⋯ai+2ai+1ai⋯an';
MathJaxMap['math_154'] = '19a3a4⋯a10';
MathJaxMap['math_155'] = '33a3a4⋯a10';
MathJaxMap['math_156'] = 'abc→cba';
MathJaxMap['math_157'] = 'a1a2…a10a118';
MathJaxMap['math_158'] = 'a1a2⋯a10a116';
MathJaxMap['math_159'] = 'X';
MathJaxMap['math_160'] = '11a3a4⋯a16';
MathJaxMap['math_161'] = '55a3a4⋯a16';
MathJaxMap['math_162'] = '22a3a4⋯a16';
MathJaxMap['math_163'] = '55a3a4⋯a16';
MathJaxMap['math_164'] = 'a1a2⋯a16';
MathJaxMap['math_165'] = 'a1a2⋯a13a1434';
MathJaxMap['math_166'] = 'a1a2⋯a13a145';
MathJaxMap['math_167'] = '83a3⋯a154';
MathJaxMap['math_168'] = '19a3⋯a15';
MathJaxMap['math_169'] = '90a3a4⋯a16';
MathJaxMap['math_170'] = '90a3a4⋯a16';
MathJaxMap['math_171'] = '47a3⋯a15a16';
MathJaxMap['math_172'] = 'x−4';
MathJaxMap['math_173'] = 'x+6';
MathJaxMap['math_174'] = 'x';
MathJaxMap['math_175'] = '83a3⋯a15a16';
MathJaxMap['math_176'] = '18a3⋯a15a16';
MathJaxMap['math_177'] = '114180 − 114150 = 30';
MathJaxMap['math_178'] = '⋯abc⋯→⋯cba⋯';
MathJaxMap['math_179'] = '751⋯→157⋯';
MathJaxMap['math_180'] = 'a9';
MathJaxMap['math_181'] = '3a1+7a2+a3+3a4+7a5+a6+3a7+7a8';
MathJaxMap['math_182'] = 'c1';
MathJaxMap['math_183'] = 'c2';
MathJaxMap['math_184'] = 'c2=0';
MathJaxMap['math_185'] = 'c1=0';
MathJaxMap['math_186'] = 'c2=10−c1';
MathJaxMap['math_187'] = 'a1a2a3a4';
MathJaxMap['math_188'] = 'a5';
MathJaxMap['math_189'] = 'a1+2a2+a3+2a4+a5';
MathJaxMap['math_190'] = '(10a1+9a2+8a3+...+a10)−(10a3+9a2+8a1+...+a10)';
MathJaxMap['math_191'] = '2a1−2a3=2(a1−a3)';
MathJaxMap['math_192'] = '2(a1−a3)';
MathJaxMap['math_193'] = 'a1−a3';
MathJaxMap['math_194'] = 'a1−a3=0';
MathJaxMap['math_195'] = 'a10';
MathJaxMap['math_196'] = 'a1+2a2+3a3+4a4+5a5+6a6+7a7+8a8+9a9+10a10';
MathJaxMap['math_197'] = '⋯72⋯';
MathJaxMap['math_198'] = '⋯27⋯';
MathJaxMap['math_199'] = '⋯ab⋯→⋯ba⋯';
MathJaxMap['math_200'] = '3⋅2+7=23';
MathJaxMap['math_201'] = '7+3⋅2=13';
MathJaxMap['math_202'] = '3⋅2+7=13';
MathJaxMap['math_203'] = '2+7⋅3=23';
MathJaxMap['math_204'] = '3⋅2+6=12';
MathJaxMap['math_205'] = '3⋅6+2=20';
MathJaxMap['math_206'] = '2+3⋅6=20';
MathJaxMap['math_207'] = '6+3⋅2=12';
MathJaxMap['math_208'] = 'ab';
MathJaxMap['math_209'] = 'ba';
MathJaxMap['math_210'] = 'a−b';
MathJaxMap['math_211'] = 'a12';
MathJaxMap['math_212'] = 'a1a2⋯a11';
MathJaxMap['math_213'] = '12a1+11a2+10a3+9a4+8a5+7a6+6a7+5a8+4a9+3a10+2a11+a12';
MathJaxMap['math_214'] = 'b';
MathJaxMap['math_215'] = 'a';
MathJaxMap['math_216'] = 'a';
MathJaxMap['math_217'] = 'b';
MathJaxMap['math_218'] = 'a';
MathJaxMap['math_219'] = 'b−a';
MathJaxMap['math_220'] = 'w';
MathJaxMap['math_221'] = 'w';
MathJaxMap['math_222'] = 'w';
MathJaxMap['math_223'] = '(7w+3+2w+1+5w+6+7w+4)−(7w+3+2w+1+5w+6+6w+1)';
MathJaxMap['math_224'] = 'w+3';
MathJaxMap['math_225'] = 'w=7';
MathJaxMap['math_226'] = 'a';
MathJaxMap['math_227'] = 'b';
MathJaxMap['math_228'] = 'a';
MathJaxMap['math_229'] = 'b';
MathJaxMap['math_230'] = '26⋅73=8918';
MathJaxMap['math_231'] = 'm';
MathJaxMap['math_232'] = 'b';
MathJaxMap['math_233'] = '40(m−1)+b+500';
MathJaxMap['math_234'] = '40(m−1)+b+600';
MathJaxMap['math_235'] = '+2a7+a8+2a9+a10+2a11+a12+2a13+a14+2a15+T+a16';
MathJaxMap['math_236'] = '+0+2⋅1';