一部は重なる(0以外の)4つの数字から四則演算だけで10を作りたい
結果の表示の原則は
和の結合法則と、和と積の交換法則は無視している。つまり，それだけを除いて同じものは1種類だけを挙げるようにしている．
*1 と /1 も同じとしている。また，1* は他の数のどこにおいても同じなので，それだけの違いの場合，原則としてそのうちの1つだけを挙げている．（つまり，正しいリストでは，1を含んでいて，他の3つで10を作れるような場合には，好きな箇所に 1* をすることができるので，1種類だけあげる，またはその際の 1* を表示しないというやり方も考えられる．）
ただし，何ヶ所かでは，とくに最初の方では，上の基準では同じであっても見た目がかなり違っているような場合には，できるだけ挙げて参考に供することにしている．そういう場合は，(=****)という書き方をしたつもりである．したがって，以下のリストでは必ずしも式の候補の採り方に一貫性はない．それが嫌なら，適当にルールを決めることになるが，立場によって，挙げるもの，挙げる順序には好みが出てくるだろう．
途中の段階で負の数がでる形のものは，負の数を作らない順序のものがあれば，それだけを採取している。
また， a*b/cは (a*b)/c だけでなく (a/c)*b=a*(b/c)=a/(c/b)= b/(c/a) などの表示を持つが，()の中が整数になるような場合は，特に小学生にとっては違うものと認識されるだろうから，あげるようにした。
同様に括弧のつけ方だけの表示の違いは一般に同じものとみなすことにしているが，括弧の中が整数になる場合，一歩一歩の計算の積み重ねとしての違いを意識する場合が考えられるので，あげるようにした。
重なる場合で，インチキをしないといけない場合は，四則だけでできない場合に限ってあげることにした．インチキといっても，10進記数法とベキを使う以外は認めていない．logと階乗を認めてもそれほど増えるわけではないが，ガウス記号を使えばなんとかすべての組合せに対して答えを得ることはできる．
以下の先頭に＊が付いていないものは，四則演算のみで答えが得られるもので，付いているものはそれ以外の方法を使ってのみ答えが得られているものである．
少しでも，＊を取り除いていきたいと考えている．
＊1111-> 11-1*1=(11-1)*1
＊1112-> 11+1-2= 12-1-1 = 21-11
＊1113 -> 1+3^{1+1} = 3!+1*(1+1)!
1114-> (1+1)*(1+4)
1115-> 1*(1+1)*5
1116-> (1+1)*(6-1)
1117-> 1+1+1+7
1118-> 1*(1+1+8) = 8+(1+1)/1= 1*(1+\sqrt{81})
1119-> 1*1*(1+9)=1*(1+1*9)=1-1+1*9 = 9+1*1*1 = 9+1^{1-1}
＊1122-> 1+(1+2)^2 = (21-1)/2 = 1*(12-2)= 11-2/2 = (21-1)/2
1123-> 1+(1+2)*3 = (1+1)*(2+3) = 2^3+1+1= 31-21 =13-1-2
1124 -> 1+1+2*4 = 1+(4-1)^2
1125 -> 1-1+2*5 =1*1*2*5 =(1+1)*\sqrt{25}
1126 -> 1*2*(6-1) = (1+1)*6-2 =2*6-1-1
1127 -> 2*(7-1-1)
1128 -> 1-1 + 2+8 =1*1*(2+8) = 1+18/2
1129 -> 1*(9+2-1) = 9+1^{2-1} = 9+2^{1-1} = (1+19)/2 = (9+11)/2
1133-> 1*3*3+1=1+3^{3-1} =(31-1)/3
1134-> 3*4-1-1 = (1+1)*3+4 = 1+3*(4-1) = 41-31 =14-1-3
1135-> 1*(3-1)*5
1136-> (3-1)*(6-1)
1137-> 1-1+3+7 = 1*3+1*7 = 1*1*3+7 = 3+1*1*7 = 1*1*(3+7) = 3*7-11
1138-> 1*(3+8-1) = (1+1)*(8-3)
1139-> 3+9-1-1 = 9+3^{1-1}
1144-> 1+1+4+4 =(41-1)/4
1145-> 1*(1+4+5) = 4*5/(1+1)=51-41 =15-1-4
1146-> 1-1+4+6 = 1*1*(4+6)
1147-> 1*(7+4-1)=(1+1)*7-4
1148-> 4+8-1-1 = 8*(1+1/4)
1149-> (1+1)*(9-4)= 9+4^{1-1} = 9+1*1^4
1155-> 1*1*(5+5) = 1-1+5+5 = (51-1)/5 =1*(15-5)
1156-> 1*(5+6-1) = 61-51 =16-1-5
1157-> 5+7-1-1
＊1158-> 5*\sqrt{8/(1+1)} = 1*(8+\sqrt{5-1}) =1+8+1^5
＊1159-> 1+9+[1/5] =1+1+5+\sqrt{9}= 9+5^{1-1}= 1*9+1^5= 9+1*1^5
1166-> 6+6-1-1 =11-6/6 = (61-1)/6 = 1*(16-6)
1167-> 7+6/(1+1)=71-61 =17-1-6
1168-> (1+1)*8-6 = 8/(1+1)+6
＊1169-> 1+9+[1/6] =1*1+6+\sqrt{9} = 9+6^{1-1} = 1*(9+1^6) = [11-6/9]
＊1177-> 7+[7/(1+1)] = 11-7/7 = (17-7)*1 =(71-1)/7
＊1178-> 1+8+1^7=81-71 ＝18-1-7
＊1179-> 1+9+[1/7] = 1+7+\sqrt{9}-1= 1*1*(7+\sqrt{9}) = 9+7^{1-1} = 9+1*1^7 = 9+1^{7+1} = 9+1^{7-1}
1188-> 1*1+(1+8)=1+1*(1+8)=(18-8)*1=11-8/8=(81-1)/8
*1189-> 1+9+[1/8] = 91-81 = 1+ 81/9 = 19-1-8 = 18+1-9 = 9+8^{1-1} = 9+1*1^8
1199-> (1+1/9)*9 = 1+9+[1/9] = 11- 9/9 = (91-1)/9 = 1*(19-9) = 9+9^{1-1} =(91-1)/9 = 1*(1+\sqrt{9*9})
1222-> (1+2+2)*2 = (1+2*2)*2 = 22-12 = 22/2-1
1223-> 1*2*(2+3) = 2*(1+3)+2
1224-> 4*(2+1/2) = 1*2*4+2 = 2*4+1*2 = (4!-2!)/2-1 = 4+12/2
1225-> 1+2+2+5=1+2*2+5 = 5*(1+2/2) = 2*(5-1)+2 = 2*(5+1)-2 = 1+(5-2)^2
1226-> 1*(2+2+6) =1*(2*6-2) = 2+16/2
1227-> 7+2+2-1=7+2*2-1 = 1*2*(7-2)
1228-> 2*(1+8/2) = 1+8+2/2 =(2-1)*(2+8) = (2+18)/2 = (8+12)/2
1229-> 9+1*2/2 = 1+9*2/2 = (1+9)*2/2
1233-> 1+2*3+3=3*3+2-1 =23-13 =3+21/3
1234-> 1+2+3+4= 1*2*3+4= 1*4+2*3= 1*(2*3+4)= 2*4+3-1= 1*(3*4-2)= 1*3*4-2= 3*4-1*2= (3-1/2)*4= (1+3/2)*4= 2+4*(3-1) = 3+14/2
1235-> 2*3+5-1= ((1+3)*5)/2= 1*(2+3+5)= 1*3+2+5
= 1*2+3+5= 2+3+1*5= 1*(2+5)+3= 2+1*(3+5)= 1*(2+3)+5= 3*(5-1)-2=1+3*(5-2)= 5*((1+3)/2)= (1+3-2)*5= 5/(3/2-1)
1236-> 2+3+6-1= 1+2*6-3= 1+3*(6/2)= 1+(3*6)/2= 6*(1+2/3)
= 6*(2-1/3)=2*(3-1)+6= (3-1)*6-2 =6+12/3
1237-> 2*7-1-3= 2*(1+7-3)= (3*7-1)/2= (2-1)*(3+7)= (2-1)*3+7= 3+(2-1)*7 = 1+27/3 = (3+17)/2 = (7+13)/2
1238-> 1+3+8-2= 1*2*(8-3)= 2*(1*8-3)= 2*(8-1*3)= 8+(1+3)/2
1239-> 2*(9-1-3)= 1*(3+9-2)= 3+9-1*2= 1*3+9-2= 3+1*9-2= 3+9-1*2= 1*(3+9)-2= 1*(9-2)+3= 9+3/(1+2)= 9+(1+2)/3= 9+2/(3-1)= 9+(3-1)/2= 1*(3-2)+9= (1+9)*(3-2)= 1+9*(3-2)
= (21+9)/3 = (29+1)/3
1244-> (1+4)*4/2 = 24-14
1245-> 2+4+5-1= 1*4*5/2= 1*5*(4/2)= 1*5*(4-2)= 5*(1*4-2)= 5*(4-1*2) = 2^4-1-5= 4^2-1-5
1246-> (6-1)*(4-2)= (6-1)*(4/2)= (2-1)*(6+4)= 6+(2-1)*4= (2-1)*6+4= 2*(1+6)-4 = (4+16)/2 = (6+14)/2
1247-> 1+4+7-2= 2*7-1*4= 1*2*7-4(= 7/(1/2)-4)= 1*(2*7-4)= 1+7+4/2 = (7/2-1)*4 = 7+12/4
1248-> (1+8-4)*2= 1*8+4/2= 1*(8+4/2)= 8+1*4/2= 8+4/(1*2)= 1*(4+8-2)= 1*4+8-2= 4+1*8-2= 4+8-1*2= 1*(4+8)-2= 1*(4-2)+8= 4+1*(8-2)= 2*(8-1)-4
1249-> 4+9-1-2= 9-1+4/2= 1*2*(9-4)= 2*(1*9-4)= 2*(9-1*4)
1255-> 5+5*(2-1)=(1+2)*5-5 = (15+5)/2 = 25-15
1256-> 1+5+6-2= (5*6)/(1+2)= 5*(6/(1+2))= 5*(6/2+1)= 2/(6/5-1)= 6/(1-2/5)
1257-> 2*7+1-5= 1*(5+7-2)= 1*5+7-2= 5+1*7-2= 5+7-1*2= 1*(5+7)-2= 1*(5-2)+7= 5+1*(7-2)= 7+(1+5)/2 = (1+7^2)/5
1258-> 5+8-1-2= 2*8-1-5= 1+5+8/2= 8+(5-1)/2
1259-> 5+(9+1)/2= 2*(1+9-5)
1266-> 6+6-2*1=1*6+6-2 = 26-16
1267-> 6+7-1-2= 6+(1+7)/2= 1*(7+6/2)= 1*7+6/2= 7+1*6/2= 7+6/(1*2)= 2*(1+7)-6
1268-> 6/2-1+8= 1*6+8/2= 1*(6+8/2)= 6+1*8/2= 6+8/(1*2)
= 1*(2*8-6)= 1*2*8-6= 2*8-1*6= 1*(2*8-6)= 8+6/(1+2)= (1+2)*6-8
=8+12/6
1269-> (9-1)/2+6= 2*(9-1)-6
1277-> 7*(1+2/7) = 27-17 =7+21/7
1278-> 2*8+1-7= 8/2+7-1 =1+72/8
1279-> 9*2-1-7= 7+9/(1+2)
1288-> (1+2/8)*8 =28-18
1289-> 1*(2*9-8)= 1*2*9-8= 2*9-1*8= 1*2*9-8 =(9^2-1)/8
1299-> 1+2*9-9 = 1+(9+9)/2=29-19
1333-> (3+1/3)*3 = 3*3+1^3 = 1+3^3/3 = 33/3-1
1334-> 1*(3+3+4) = 3*4+1-3 = 3*3+1^4
1335-> (1+3/3)*5
*1336-> 16-3-3 = 3*3+1^6
1337-> (1+7/3)*3 = (3+7)*1^3
1338-> (3-1)*(8-3)
1339-> (1+9)*3/3 =1*3/3+9=1+9*3/3
1344-> 4+4+3-1
1345-> (4*5)/(3-1)= 5*(4/(3-1))= 5*(1+4-3)= (1+4)*(5-3)= 3*5-1-4= 3*(1+4)-5= 4/(1-3/5)
1346-> (6/3)*(1+4)= (6*(1+4))/3= 4*(1+3)-6 = 1+36/4
1347-> 1+(7-4)*3=(3-1)*7-4
1348-> 1+4+8-3= 8+4/(3-1) =4+18/3 = (3^4-1)/8
1349-> (3-1)*(9-4)= 1*(4+9-3)= 1*(4+9)-3= 1*(4-3)+9= 1+9*(4-3)= (1+9)*(4-3)= 4+1*(9-3)= 1*4+9-3= 4+1*9-3= 4+9-1*3= 9+4/(1+3)= 9+(1+3)/4= 9+3/(4-1)= 9+(4-1)/3
= (31+9)/4 = (39+1)/4 =1*(3+\sqrt{49})
1355-> 3*5-1*5 = 5+15/3
1356-> 1+3*5-6= (5-3)*(6-1)= 1*(5*6)/3= 1*5*(6/3)= 5*(6/(1*3))= 5*((1*6)/3)= 5*(6-1-3)= 3*(6-1)-5
1357-> 1+5+7-3= (5*(7-1))/3= 5*((7-1)/3)
1358-> 1*(5+8-3)= 1*5+8-3= 5+1*8-3= 5+8-1*3= 1*(5+8)-3
= 5+1*(8-3)= 8+1*(5-3) = 3*(1+5)-8= 1+3*(8-5)= (5*8)/(1+3)
= 5*(8/(1+3))= 8+(1+5)/3
1359-> 5+9-1-3= 5*(9/3-1)
1366-> 6+6+1-3 = 1+3+\sqrt{6*6}
1367-> 1*(6+7-3)= 1*6+7-3= 6+1*7-3= 6+7-1*3= 1*(6+7)-3
= 6+1*(7-3)= 1*(6-3)+7= 1*(6+7)-3= 7+6/(3-1)= 3*6-1-7= 1+7+6/3 = 1+63/7
1368-> 6+8-1-3= 1*(3*6-8)= 3*6-1*8= 1*3*6-8= 1*(8+6/3)= 1*8+6/3= 8+1*6/3= 8+6/(1*3)= 6+8/(3-1)= 6*(8/3-1)= (3-1)*8-6
1369-> 3*(9-6)+1= 3*6+1-9= 1+6+9/3= 9-1+6/3
1377-> (1+3/7)*7 =1*(3+\sqrt{7*7})
1378-> 8+(7-1)/3= 7+(1+8)/3= 3*(7-1)-8
1379-> 1*(7+9/3)= 1*7+9/3= 7+1*9/3= 7+9/(1*3)
1388-> 8+8/(1+3) =3+8-1^8
1389-> 8-1+9/3= (3-1)*9-8
＊1399-> 1+9+[3/9] = 9+1^{3+9} ＝ 1*(9+\sqrt{9}/3)
＊1444-> (1+4)*4/\sqrt{4} = 4*(4-1)-\sqrt{4} = 1*(4+4)+\sqrt{4} = 44/4-1
1445-> (1+4/4)*5 = 4*4-1-5 = 1+45/5
1446-> (1+6/4)*4=(1+4)*(6-4) = 1*(4*4-6)
1447-> 4*4+1-7 = 7-1+\sqrt{4*4}
1448-> 1+8+4/4 = (1+4)*8/4
1449-> 1+4+9-4 = (1+9)*4/4 =4+4-1+\sqrt{9}
1455-> (4-1)*5-5 = 1+45/5 = 4+5+1^5 =(5+5)*1^4
1456-> 4*(5-1)-6= 1*5*(6-4)= 5*(1*6-4)= 5*(6-1*4)= (5*6)/(4-1)= 5*(6/(4-1))= 5/(6/4-1)) = 1+54/6
1457-> (1+4)*(7-5)= 5*(7-4-1)= (5*(1+7))/4= 5*((1+7)/4)= 4/(7/5-1)
1458-> 1+5+8-4= (1*5*8)/4= 1*((5*8)/4)= 1*(5*(8/4))= (5*8)/(1*4)
= 5*((1*8)/4)= 5*(8/(1*4))
1459-> 4*5-1-9= 1*(5+9-4)= 1*5+9-4= 5+1*9-4= 5+9-1*4= 1*(5+9)-4
= 5+1*(9-4)= 9+1*(5-4)= (1+9)*(5-4)= 1+9*(5-4)= ((9-1)*5)/4= 5*((9-1)/4)
= 9+(1+4)/5= 9+5/(1+4)= 9+(5-1)/4= 9+4/(5-1)
= (41+9)/5 = (49+1)/5
1466-> (1+4/6)*6 = 6+16/4 = 4+6+1^4
1467-> 1+6+7-4
1468-> (8-6)*(1+4)= ((6-1)*8)/4= (6-1)*(8/4)= 8+6/(4-1)= (4-1)*6-8
= 1*(6+8-4)= 1*6+8-4= 6+1*8-4= 6+8-1*4= 1*(6+8)-4= 6+1*(8-4)= 1*(6-4)+8
1469-> 6+9-1-4= (1+9/6)*4
1477-> 7+7-1*4
1478-> 7+8-1-4= 1+7+8/4= 8+(1+7)/4 = 8+14/7
1479-> (9-7)*(4+1)= 7+9/(4-1)
1488-> 1*(8+8/4) = 1*[84/8] = 1*(\sqrt{4}+\sqrt{8*8})
1489-> 8/4+9-1= 8+(9-1)/4 = (9/4-1)*8
＊1499-> 1+9+[4/9] = 9+1^{4+9} = 9+[9/(1+4)]
1555-> (1+5/5)*5 = 55/5-1
1556-> 5*(1+6-5) = 5+6-1^5
1557-> 1*5*(7-5) = 7+15/5
1558-> 5*(8-1-5) =1+8+5/5
1559-> (1+9)*5/5
1566-> 5*(1+6/6)
1567-> (1+7-6)*5= (6-1)*(7-5)
1568-> 1+6+8-5= 1*5*(8-6)= 5*(8-1*6)= 5*(1*8-6)= 6/(8/5-1)
1569-> 5*(9-6-1)= 1*(6+9-5)= 1*6+9-5= 6+1*9-5
= 6+9-1*5= 1*(6+9)-5= 1*(6+9)-5= 6+1*(9-5)
= 9+(1+5)/6= 9+6/(1+5)= 9+(6-1)/5= 9+5/(6-1)
= 1*(6-5)+9= (6-5)*(1+9)= 1+9*(6-5)= 5/(9/6-1)
= (51+9)/6 = (59+1)/6
1577-> (7*7+1)/5=5*(1+7/7) = 1+7+7-5
1578-> 5*(8-7+1)= 1*(7+8-5)= 1*7+8-5= 7+1*8-5
= 7+8-1*5= 1*(7+8)-5= 1*(7-5)+8
1579-> 1*5*(9-7)= 5*(9-1*7)= 5*(1*9-7)= 7+9-1-5
1588-> 8+8/(5-1)=5*(1+8/8)
1589-> (1+9-8)*5= 8+(1+9)/5
1599-> 5*(1+9/9) = 1+5+9-5
＊1666-> 1+6+ [\sqrt{6+6}] = 66/6-1 = \sqrt{6*6}+\sqrt{16}
＊1667-> 1+6+[\sqrt{6+7}] =1+[66/7] = [67/6]-1
1668-> 1+8+6/6
1669-> (1+9)*6/6 = 1+6+9-6 = (1+6/9)*6
＊1677-> 1+[67/7]= 1*[76/7]
1678-> 1+7+8-6 = 7+18/6
1679-> 1*(7+9-6)= 7+9-1*6= 7+1*9-6= 1*7+9-6= 1*(7+9)-6
= 7+1*(9-6)= 1*(7-6)+9= 1+9*(7-6)= (1+9)*(7-6)= (6-1)*(9-7)
= 9+(1+6)/7= 9+7/(1+6)= 9+(7-1)/6= 9+6/(7-1)
= (61+9)/7 = (69+1)/7
1688-> 1*(8+8-6) = 8+16/8
1689-> 8+9-1-6
＊1699-> 1+9+[6/9] = 9+1^{6+9}=9+1^{9-6}=9+1^{6*9}
＊1777-> 7+[\sqrt{1+7+7}] = 77/7-1
1778-> 1+8+7/7 = 1+(7!+8!)/7!
1779-> (1+9)*7/7
1788-> 8+8+1-7
1789-> 1*(8+9-7)= 8+9-1*7= 8+1*9-7= 1*8+9-7= 1*(8+9)-7
= 1*(8-7)+9= 8+1*(9-7)= (8-7)*(1+9)= 1+(8-7)*9
= 9+(1+7)/8= 9+8/(1+7)= 9+(8-1)/7= 9+7/(8-1)
= (71+9)/8 = (79+1)/8
1799-> 9+9-1-7=9+1^{7+9}=9+1^{7*9}=9+1^{9-7}
1888-> 1+8+8/8 = 88/8-1
1889-> (1+9)*8/8 = 8+18/9 = 1* (8!+9!)/8!
1899-> (1+9)*(9-8) = (9*9-1)/8 = (81+9)/9 = (81+9)/9
1999-> 1+9+9-9=1*9+9/9=9+1*9/9 = (1+9)*9/9 =((1+9)!-9!)/9! = 9+1^{9+9} = 9+1^{9-9} = 9+1^{9*9} = 99/9-1
2222-> 2+2*2*2 = 2*(2+2)+2 = (22-2)/2
2223-> 2*2+2*3 = 2+2+2*3 = 32-22
2224-> 2*(4+2/2) = 2*(2+4)-2 = (4!-2)/2-2
2225 -> 2*2*5/2 = 5*(2+2-2)
2226 -> 2*(6-2/2) = 2*(2+6/2)= 2*(6-2)+2
2227 -> 2+7+2/2 = 2*7-2-2 = 2*7-2*2
2228 -> (2+8)*2/2 = 8+(2+2)/2 = 8+2*2/2 = 2*(8-2)-2
2229 -> 2+9-2/2 = (2+2*9)/2 = (9^2+2)/2
2233 -> 3*3+2/2=2+2+3+3 = 2*(3+3)-2 = (23-3)/2 = (32-3)/3
2234 -> 2*(3+2/4) = (2+3)*4/2 = 2+24/3 = 2+32/4 =42-32 = 2^4-2*3 = 4^2-2*3
2235 -> 2*5*(3-2) = 5*(3-2/2) = (2^5-2)/3
2236 -> 3+6+2/2 = (3*6+2)/2
2237 -> (3+7)*2/2
2238 -> 3+8-2/2 = 2*8-2*3 =(2+8)*(3-2) = (22+8)/3 = (28+2)/3
2239 -> (2*9+2)/3 = 9+2*2-3=9+(3-2)^2=9+(2/2)^3
2244-> 4*(2+2/4) = (24-4)/2 = (42-2)/4 = 2^4-2-4 = 4^2-2-4
2245 -> 4+5+2/2 = 52-42
2246 -> (4+6)*2/2= \sqrt{2+2}+\sqrt{64}= \sqrt{2*2}+\sqrt{64}
2247 -> 2*(7-4/2) = 7+(2+4)/2
2248 -> 2*8-2-4
2249 -> 9+2*2/4
2255 -> (5+5)*2/2 = (25-5)/2 = (52-2)/5 = (5^2-5)/2
2256 -> 5*(6-2-2) = 62-52
2257 -> (5+7)/2-2
2258 -> 5*8/(2*2)
2259 -> 5+9-2-2=5+9-2*2
2266-> (2-2/6)*6 = (26-6)/2 = (62-2)/6
2267 -> 2*7+2-6 = 72-62
2268 -> 2*(8-6/2) = (2*8+6)/2
2269 -> 2*9-2-6 = 9+6^{2-2} = 9+(2/2)^6
2277 -> 7+7-2-2 = (72-2)/7 = (27-7)/2
2278 -> 2*7-8/2 = 72-62
2279 -> 2*(2*7-9) = 2+(7+9)/2 = 9+(2/2)^7 = 2+72/9
2288 -> 2*8+2-8 = (28-8)/2 = (82-2)/8 = \sqrt{2+2}+\sqrt{8*8}) = \sqrt{2*2}+\sqrt{8*8})
2289 -> 2*(9-8/2) = 92-82
2299 -> (2+9+9)/2 = 9+9^{2-2}=9+(2/2)^9 = (29-9)/2 = (92-2)/9
2333-> 3*3+3-2 =33-23
2334-> 3*(4-2/3) = 3*(2+4/3) = 2^4-3-3 = 4^2-3-3
2335-> 2*3*5/3 = 3*5-2-3
2336-> (2+3)*6/3 =(3+2/6)*3
2337-> 2+7+3/3 = (3+7)*(3-2) = 3*(7-3)-2
= (23+7)/3 = (27+3)/3 =(3^3-7)/7 = (2+3)*\sqrt{7-3}
2338-> (2+8)*3/3 = 2*8-3-3
2339-> 9+(3-2)^3=9+(3/3)^2
2344-> 4*(3-2/4) = 4*4-2*3 =3*4+2-4 = 34-24
2345-> 3+4+5-2= (4-3)*2*5= 3+5+4/2= 2*4+5-3
= ((2+4)*5)/3= 5*((2+4)/3)= 5*(2*3-4)= 2+4*(5-3)
2346-> 3+4+6/2= (2+3)*(6-4)= 2+(4*6)/3= 2+4*(6/3)
= (3-2)*(4+6)= (3-2)*4+6= 4+(3-2)*6= 4+2*(6-3)= 2*4+6/3= 4*(2+3/6)
= 3*6-2*4= 2*(3+6-4)= 4*(6-3)-2= 3*(2+4/6)
= 3+42/6 = (24+6)/3 = (26+4)/3
2347-> 2+4+7-3= (2+4*7)/3= 2*(3*4-7)
2348-> 2*3+8-4= (4-2)*(8-3)= (8-3)*(4/2)= (4*(8-3))/2= 2*(3+8/4)
= (4-3)*(2+8)= (4-3)*2+8= 2+(4-3)*8= (3*8-4)/2= (3*4+8)/2= (4*8-2)/3
= (2+3)*(8/4)= ((2+3)*8)/4= 3*(2+4)-8= (2-3/4)*8= 3*(8-4)-2= 8+(2+4)/3
= 3+28/4= (32+8)/4 = (38+2)/4
2349-> 2+3+9-4= 4+2*(9/3)= 3+9-4/2= (4*9)/3-2= 4*(9/3)-2
2355 -> (5+5)*(3-2) = (3*5+5)/2 = (25+5)/3 = 35-25 = (5^2+5)/3
2356-> 2+5+6-3= 2*6+3-5= 2*(5-3)+6= (5-3)*6-2= 2*(3+5)-6= 6+(3+5)/2
2357-> 3*(7-2)-5= 5*(7-2-3)= 2*(7+3-5)= (7-5)*(2+3)
= (5-3)*(7-2)= 3*5+2-7= 5+(3+7)/2= 5*((7-3)/2)= (5*(7-3))/2= 3*(7-2)-5
2358-> (5*(8-2))/3= 5*((8-2)/3)= 5*(8-2*3)= 8+(5-2)/3
2359-> 9/3+5+2= 2*3+9-5= 2*9-3-5= 9+(2+3)/5= 9+5/(2+3)
= 9+(5-2)/3= 9+3/(5-2)= 9+(5-3)/2= 9+2/(5-3)= 3*(9-5)-2
2366 -> 2+6+6/3 = 3*6-2-6 = 2*6 -6/3 = 36-26 = (6^2-6)/3
2367-> ((7-2)*6)/3= (7-2)*(6/3)= (7-6/3)*2
2368-> 2*(8+3-6)= (2+3)*(8-6)= 2*(3+6)-8= 3+(6+8)/2= 3*(2+8/6) = 6+32/8
2369-> 6+9-2-3= 2*((6+9)/3)= (2*(6+9))/3 = (2-3/9)*6 = 9+(2*3)/6= 9+6/(2*3)= 9+(6/2)/3= 9+(6/3)/2=(2+6/9)*3
2377 -> 2*7+3-7 = 37-27
2378-> 7+8-2-3= 3*8-2*7= 2*((7+8)/3)= (2*(7+8))/3
2379-> (2+3)*(9-7)= 2*(3+9-7)= (3*9-7)/2= 3*7-2-9= 7+9-2*3= 7+(9-3)/2
2388 -> 8+8-2*3 = 2*8 -2*3 = 38-28
2389-> 8/2-3+9= 2*8+3-9= 2*(8-9/3)= (3+8+9)/2
2399 -> 9+9/3-2 = 9+[9/(2+3)] = 3^2+9/9 = 9+[9/(2+3)] = 9+(3-2)^9 = \sqrt{9*9}+3-2 = 39-29
2444 -> 4+4+4/2 = 4+4+4-2 = 2*(4+4/4) = (4+4*4)/2 = 4*4-2-4 = 4+24/4 = (4!-4)*2/4 = (4!-4)/(4-2)
2445 -> 2*4*5/4 =4+2*5-4
2446 -> 6+(4+4)/2 = 2*4+6-4 = (4*6-4)/2 = (4+6^2)/4
2447 -> 2+7+4/4 = 7*(4-2)-4 = 4+42/7
2448 -> (2+8)*4/4 = 4+8-4/2 = (2+4/8)*4
2449 -> 9+2-4/4
2455 -> 2*5*(5-4) = 2+4-5/5 = 4*5-2*5
2456-> (4*2-6)*5= 2*(4+6-5)= 5+(4+6)/2= (5*(2+6))/4= 5*((2+6)/4)= 5/(2-6/4)
2457-> 2+5+7-4= 4*2+7-5= 2+4*(7-5)= 5+7-4/2= 5/(4-7/2)
2458-> 2*(5+4)-8= 5*((8-4)/2)= (5*(8-4))/2= 4*5-2-8= 4*(8-5)-2= 4+2*(8-5)= 2*(5-4)+8= (2+8)*(5-4)= 2+8*(5-4)= 8+(2+6)/4= 4/(2-8/5)
= (42+8)/5 = (48+2)/5 =(2^5+8)/4
2459-> 2+4+9-5= 5/(9/2-4)
2466 -> 6+6+2-4 = (4*6-4)/2 = 6+24/6 =(2^6-4)/6
2467-> (7-2)*(6-4)= 7+6/(4-2)= 7+(2*6)/4= 2*(4+7-6)= 4*6-2*7= (6*7-2)/4= (6-7/2)*4
2468-> 2*4+8-6= 2+6+8/4= (6*8)/4-2= 6*(8/4)-2= 4*(8/2)-6= (4-2)*8-6
= (4*8)/2-6= (4/2)*8-6= 2*6-8/4= 8/(4-2)+6= 2+4*(8-6)= 8+(2+6)/4 =2+48/6 =2+64/8 = (8^2-4)/6
2469-> 9+(6-4)/2= 9+(6-2)/4= 9+(2+4)/6= 9+2/(6-4)= 9+4/(6-2)= 9+6/(2+4)= 4+2*(9-6)= 4+9-6/2= 4*(9-6)-2
2477-> (2-4/7)*7
2478-> 2*(8-7+4)= 2*7+4-8= (4*7-8)/2= (8*(7-2))/4= (7-2)*(8/4)= (7-8/4)*2 = 7+24/8
2479-> 9-4+7-2= 4*7-2*9= 2*4+9-7= 2+4*(9-7)= (4+7+9)/2= (7-9/2)*4= 2*(9-7)+4 = (7^2-9)/4
2488 -> 2*(4+8/8)
2489-> 9+(2*4)/8= 9+8/(2*4)= 9+(8/2)/4= 9+(8/4)/2= 2*(4+9-8)
= (4*9)/2-8= (4/2)*9-8= (4-2)*9-8
2499 -> 2*(4+9/9)
2555 -> 2*5*5/5 = (5*5-5)/2 = 5+25/5 = 5+5^2/5 = \sqrt{25}+ \sqrt{5*5}
2556 -> 2*5*(6-5)
2557 -> 2+7+5/5
2558 -> (2+8)*5/5
2559 -> (9-5)*5/2 = 9+(5/5)^2
2566 -> 2*5*6/6 = 2*(6!-5!)/5!
2567-> 2+6+7-5= 2*5*(7-6)= 5+2*6-7= 2*(7-5)+6= (7-5)*6-2 = 2+56/7
2568-> (5-2)*6-8= (5*8)/(6-2)= 5*(8/(6-2))= (2+6*8)/5
= 5+8-6/2= 8+6/(5-2)= 8+2*(6-5)= (8+2)*(6-5)= 2+8*(6-5)= 8/(2-6/5)
= (52+8)/6 = (58+2)/6
2569-> 2+5+9-6= (5+6+9)/2= 4+2*(9-6)= 5/(2-9/6)
2577 -> 2*5+7-7=2*5*7/7
2578-> 2*5*(8-7)= (5+7+8)/2
2579-> 2*7+5-9= 9+(2+5)/7= 9+(7-2)/5= 9+(7-5)/2= 9+7/(2+5)= 9+5/(7-2)= 9+2/(7-5)
2588 -> 2*5+8-8=2*5*8/8
2589-> 2*5*(9-8)= 8+(9-5)/2= 8+9-2-5= 5+9-8/2
2599 -> 2*5+9-9=2*5*9/9
2666 -> 2*(6-6/6)=2+6+\sqrt{6*6} = 6*6-26
2667 -> 2+7+6/6 = (6+2^6)/7 = 2+(7!+6!)/6!
2668 -> (2+8)*6/6
2669 -> 2+9-6/6
2677 -> 2+7+7-6
2678-> (7-2)*(8-6)= 2*(6+7-8)= (2+8)*(7-6)= 2+8*(7-6)= 2*(7-6)+8 = 6+28/7 = (62+8)/7 = (68+2)/7 = (8^2+6)/7
2679-> 2+6+9-7= 7+2*9/6= 2*6+7-9= 2*(9-7)+6= (9-7)*6-2
2688-> (2-6/8)*8
2689-> (6+8-9)*2= (8*9)/6-2= 9+(2+6)/8= 9+(8-6)/2= 9+(8-2)/6= 9+8/(2+6)= 9+2/(8-6)= 9+6/(8-2)
2777 -> 2+7+7/7
2778 -> (2+8)*7/7=2+7+8-7
2779 -> 2+9-7/7 = 7+27/9
2788 -> 2+7+8/8 = (72+8)/8 = (78+2)/8
2789-> 2+7+9-8= (8*9-2)/7
2799 -> 2+7+9/9
2888 -> (2+8)*8/8 = 2+8+8-8 = 2+8*8/8
2889 -> (2+8)*(9-8) = 2+(9!-8!)/8!
2899 -> 2+8+9-9=(2+8)*9/9 = 9*(2-8/9) = (82+8)/9 = (88+2)/9
2999 -> 2+9-9/9 = 9+(9/9)^2 = 9+2^{9-9}
3333 -> 3*3+3/3 = (33-3)/3 = (3+3^3)/3
3334 -> 3*3+4-3=3*3*(4-3) = 43-33
3335 -> (3+3)*5/3 = 5*(3-3/3)
3336 -> 3+6+3/3
3337 -> (3+7)*3/3=3+3+7-3 = 7+3*3/3
3338 -> 3+8-3/3 =8+(3+3)/3
3339 -> (3+3*9)/3 =3*(3+3/9) = 9+(3/3)^3
3344 -> 3*3+4/4 =4*4-3-3 = (34-4)/3 = (43-3)/4 = 3+3+\sqrt{4*4}
3345 -> 3*3+5-4 = 53-43
3346 -> 6*(3-4/3) =(4+6)*3/3 = (3+9)/3+6 =3*4-6/3=(3-3/6)*4
3347 -> (3+7)*(4-3) = 4+7-3/3= (33+7)/4 = (37+3)/4
3348 -> 3+3+8-7
3349 -> 3+4+9/3 = 9+(4-3)^3 = 9+(3/3)^4 = \sqrt{3*3}+\sqrt{49})
3355 -> 3*3+5/5＝(5-5/3)*3=(5+5)*3/3 = 3+35/5 = (35-5)/3 = (53-3)/5
3356 -> 5+6-3/3 = 3*6-3-5 = 63-53
3357-> 5*(3*3-7)
3358-> (5-3)*(8-3)
3359-> 3+3+9-5
3366-> 3*3+6/6 = (36-6)/3 = (63-3)/6
3367-> 3*3+7-6 = 7+(3+6)/3 = 73-63
3368-> (6-8/3)*3 = (3*8+6)/3
3369-> (3+9)/3+6 =3+63/9
3377-> 3*3+7/7 = (37-7)/3 = (73-3)/7 =\sqrt{3*3}+\sqrt{7*7}
3378-> 3*7-3-8=83-73
3379-> 7+9-3-3 = (3*7+9)/3
3388-> 8+8-3-3 = (38-8)/3 = (83-3)/8 = ((3*3)!+8!)/8! = 3+3+ \sqrt{8+8}
3389-> 3*3+9-8 = 9+3*3-8= 93-83
3399-> 3*3+9/9=9+3*3/9 = (39-9)/3 = (93-3)/9
＊3444-> 3*4-4/\sqrt{4} = 44-34
3445-> 4+4+(5-3) = 5*(3-4/4)
3446-> (4+6)*(4-3) = 3*(4-4/6) = 3+6+4/4 = 3*6-4-4
= (34+6)/4 = (36+4)/4 = (4^3-4)/6= \sqrt{4*4}+\sqrt{36})
3447-> (3+7)*4/4
3448-> 4+(4+8)/3 = (3-4/8)*4
3449-> 4*4+3-9
3455-> 5*(3-4/4) = (35+5)/4 = 45-35
3456-> 3+5+6-4= (3*4*5)/6= 5*((3*4)/6)= 5*(4/(6/3))= (4*5)/(6/3)= (4-6/3)*5
3457-> 3*4+5-7= 4*5-3-7= (3+7)*(5-4)= 3+7*(5-4)= 3*(5-4)+7= 4+3*(7-5)= (5-3)*7-4= (4+5)/3+7
= (43+7)/5 = (47+3)/5
3458-> 3+4+8-5= 3+5+8/4= 8+4/(5-3)
3459-> 3*5+4-9= (5-3)*(9-4)= 5*(9-3-4)= 3*(9-4)-5
3466-> 3+6+4/4 = (4*6+6)/3 = 4+36/6 = (4!+6)/(6-3) = 46-36
3467-> 4*7-3*6= 4*(7-3)-6= (6*7)/3-4= (6/3)*7-4= 6*(4-7/3) = (6+4^3)/7
3468-> (6-4)*(8-3)= 4+8-6/3= (4+8)/3+6= 3*4+6-8= 8+(3*4)/6= 3*(8-6)+4
3469-> 3+4+9-6= (4*9-6)/3= (9-4)*(6/3)= ((9-4)*6)/3= (4-6/9)*3
3477-> 3*7-4-7 = 47-37 =7+\sqrt{3*(7-4)}
3478-> (3-7/4)*8
3479-> 3*4+7-9= 9+(3+4)/7= 9+(7-3)/4= 9+(7-4)/3= 9+7/(3+4)= 9+4/(7-3)= 9+3/(7-4)= 7+(3+9)/4= 4+3*(9-7) =3+49/7
3488-> (8-3)*8/4 = 48-38
3489-> 8+9-3-4= 3+9-8/4
3499-> 4+9-9/3 = 4+(9+9)/3 = 49-39 = (3^4+9)/9
3555-> (3-5/5)*5 = 5*5-3*5 = (5*5+5)/3
3556-> 3+6+5/5
3557-> (3+7)*5/5 = 3+5+7-5 = (5*7-5)/3 =5+35/7
3558-> 3+8-5/5
3559-> 5*(5-9/3) = 9+(5/5)^3
3566-> 6+6+3-5 = 5*(3-6/6)
3567-> 3*7-5-6= 5+7-6/3= (5+7)/3+6= (3+7)*(6-5)= 3+7*(6-5)= 7+3*(6-5)= 7+6/(5-3)= 5*(3+6-7)
= (53+7)/6 = (57+3)/6
3568-> 3+5+8-6= 6+8/(5-3)= (5-3)*8-6= 5*(3+6-7) = 3+56/8
3569-> (6+9)/3+5= (3*5*6)/9= 5*((3*6)/9)= (5*(3+9))/6= 5*((3+9)/6)
3577-> 5*(3-7/7)
3578-> (8-3)*(7-5)= 5+(7+8)/3= 8+(3+7)/5= 5*(3+7-8)= (5*8)/(7-3)= 5*(8/(7-3))
3579-> 3+5+9-7
3588-> 5*(3-8/8)
3589-> (3+8-9)*5= 3*8-5-9= 9+(3+5)/8= 9+(8-5)/3= 9+(8-3)/5= 9+8/(3+5)= 9+3/(8-5)= 9+5/(8-3)= 5+8-9/3= (5-3)*9-8
3599-> 9+9-3-5 = 5*(3-9/9)
3666-> 3+6+6/6 = 6+6-6/3=(6*6-6)/3
3667-> (3+7)*6/6
3668-> 6*(3-8/6)
＊3669-> 6+36/9 = 9+[(3+6)/6] = 9+(6/6)^3 = 9+3^(6-6) = 3*\sqrt{9}+6/6
3677-> 3+6+7/7 = (63+7)/7 = (67+3)/7
3678-> 3+6+8-7= (6*(7+8))/3= (6/3)*(7+8)= 6*((7+8)/3)
3679-> 6+7-(9/3)= (7*9-3)/6= 3*(9-7)+6= 7+9/(6-3)
3688-> 3+6+8/8
3689-> 3+6+9-8= 8+(3*6)/9= 8+(3+9)/6= (6*9)/3-8= (6/3)*9-8= 6*(9/3)-8
3699-> 3+6+9/9 = 3*6-9-9
3777-> (3+7)*7/7 = 3+7*7/7 = 3+7+7-7
3778-> (3+7)*(8-7)
＊3779-> 9+[(3+7)/9] = 9+[(3+9)/7] = 7*7-39 = 73-7*9
3788-> (3+7)*8/8 = 8+8/(7-3) = (73+7)/8 = (77+3)/8
3789-> (9-8)*(3+7)= (9-8)*3+7= 3+(9-8)*7= (9-7)*(8-3)= 3+7+[8/9] = 3+8-[9/7] = (83+7)/9 = (87+3)/9
3799-> (3+7)*9/9
3888-> 3+8-8/8
3889-> 3+8+8-9 = 9+(8/8)^3
3899-> 3+8-9/9 = 9+[(3+8)/9] =9+[(3+9)/8] = 9+(9-8)^3 = 9log_3 9 -8
＊3999-> 9+[(3+9)/9] = 9+(9/9)^3 = 3*\sqrt{9} -9/9 = 9+3^{9-9}
＊4444-> 4+4+4-\sqrt{4} = 4+4+4/\sqrt{4} = 4+4+\sqrt{4}+\sqrt{4} = 4*4-4-\sqrt{4} = (4*4+4)/\sqrt{4}= (4+4/4)*\sqrt{4}=(44-4)/4
4445-> (4+4)*5/4 = 54-44 = \sqrt{4}*4*5/4
4446-> 4+4+6-4 = (4-6/4)*4 = (4+6)*4/4 = 6+4*4/4 = (4!-4)/(6-4)
4447 -> 4+7-4/4
4448 -> 8+(4+4)/4 = (4!-4)*4/8
4449 -> (4+4*9)/4=9+(4/4)^5
4455 -> 4+5+5-4=(5+5)*4/4 = (45-5)/4 = (54-4)/5
4456 -> (4+6)*(5-4)= (44+6)/5 = (46+4)/5 = 64-54 = 6+(5!-4!)/4!
4457 -> 4+4+7-5 = (4!-4)/(7-5)
4458 -> 4*4*5/8
*4459 -> 4+54/9 = 9+(5-4)^4
4466 -> (4+6*6)/4 = (46-6)/4 = (64-4)/6
= 6+6+4/\sqrt{4} = \sqrt{(4+6)(4+6)} = \sqrt{4*4}+\sqrt{6*6}
4467 -> (6-4)*7-4 = 74-64 = 7+6*\sqrt{4}/4 = (4!+6)/(7-4)
4468 -> 4+4+8-6=6+8-\sqrt{4*4}
4469 -> (4-9/6)*4 = 9+(4/4)^6
*4477 -> 4+7-[7/4] = (47-7)/4 = (74-4)/7
4478 -> 7+(4+8)/4 = 84-74
4479 -> 4+4+9-7 = 9+(4/4)^7
4488 -> 4+8 -8/4 =(4*8+8)/4 =(84-4)/8 = 4+48/8 = (48-8)/4
4489 -> 9+(4+4)/8 =9+8/(4+4) = 94-84 = 9+(4/4)^8 = (9!+8!)/(4+4)!
4499 -> 9+9-4-4 = 9+(4/4)^9 = (49-9)/4 = (94-4)/9
4555 -> 4+5+5/5 = (45+5)/5 = 55-45
4556 -> (4+6)*5/5 = 5*6-4*5
4557 -> (7-5)*7-4 =4+7-5/5 = (5*7+5)/4
＊4558 -> 5+8-\sqrt{4+5} = 4+5+[8/5] = 5+5+[4/8]
4559 -> (5*9-5)/4 = 9+(5-4)^5=9+(5/5)^4 =5+45/9
4566 -> 4+5+6/6 = (54+6)/6 = (56+4)/6 = 56-46
4567-> 4+5+7-6= (5*6)/(7-4)= 5*(6/(7-4))
4568-> (4+6)/5+8= (4*5)/(8-6)= (4/(8-6))*5= (5*(8+4))/6= 5*((4+8)/6)= 5*(4/(8-6))= (5*4)/(8-6)= 5*(4+6-8)
4569-> 4*6-5-9= (6*9-4)/5= 4*(9-5)-6
4577 -> 4+5+7/7 = 7*(7-5)-4 = 57-47
4578-> 8-7+4+5= 8+4/(7-5)= 5+7-8/4
4579-> 4*5/(9-7)= (9-4)*(7-5)= 5*(4+7-9)
4588 -> 4+5+8/8 = 58-48
4589-> 4+5+9-8
4599 -> 4+5+9/9 =9+(4+5)/9 = 59-49
4666 -> (4+6)*6/6 = 4+6+6-6 = 4+6*6/6
4667 -> (4+6)*(7-6) = 4+7-6/6 = (64+6)/7 = (66+4)/7
4668 -> 4*6-6-8=6+6-8/4
＊4669 -> 9+[(4+6)/6] = 9+(6/6)^4 = 9+4^{6-6} = (4!+6)/(9-6)
4677 -> (4+6)*7/7 = 4*6-7-7
4678-> (8-7)*(4+6)= 4*(8-7)+6= 4+6*(8-7)= (7*8+4)/6= 6*7-4*8= 8+6/(7-4)= (8-6)*7-4= 6*(7-4)-8= (4*(7+8))/6= 7+(4*6)/8 = (74+6)/8 = (76+4)/8
4679-> (7+9)/4+6
4688 -> (4+6)*8/8 = (8*8-4)/6 = (6*8-8)/4
4689-> (4+6)*(9-8)= 4*(9-8)+6= 4+6*(9-8)= (9*8)/6-4= (8-6)*(9-4)= (6-4)*9-8
4699 -> (4+6)*9/9 = (84+6)/9 = (86+4)/9
4777 -> 4+7-7/7
4778 -> 4+7+7-8
4779 -> 7*(9-7)-4 = (7*7-9)/4 = 9+(7/7)^4
4788 -> 4+7-8/8
4789-> 4+7+8-9= 8+4/(9-7)
4799 -> 4+7-9/9
＊4888 -> 8+8-8+\sqrt{4}=8+\sqrt{8*8}/4
4889 -> 8*9/4-8 = (8-\sqrt{9})*8/4 = 9+(8/8)^4 = 9+4^{8-8}
＊4899 -> 9+[(4+8)/9] = 9+[(4+8)/8] = 9+(9-8)^4
＊4999 -> 9+[(4+9)/9] = 9+(9/9)^4
5555 -> 5+5*5/5= 5*(5+5)/5=(55-5)/5= \sqrt{5*5}+\sqrt{5*5})
5556 -> (5+5)*(6-5) = 5+6-5/5 = (55+5)/6 = 65-55
5557 -> 5*7-5*5
5558 -> 8+(5+5)/5
5559 -> (5*9+5)/5 = 9+(5/5)^5
5566 -> (5+5)*6/6 = (65-5)/6 = (56-6)/5
5567 -> (5+5)*(7-6) = (65+5)/7 = 75-65
5568 -> 5*8-5*6
5569 -> 5*(5+6-9) = 5*(9-6) - 5 = 5*5-6-9 = 9+(6-5)^5=9+(5/5)^6 = 9+6^{5-5}
5577 -> (5+5)*7/7 = (75-5)/7 = (57-7)/5
5578 -> (5+5)*(8-7) = (75+5)/8 = 85-75
5579 -> 5*9-5*7=9+(5/5)^7
5588 -> (5+5)*8/8 = (85-5)/8 = (58-8)/5
5589 -> (5+5)*(9-8) = (85+5)/9 = 95-85
5599 -> (5+5)*9/9 = (95-5)/9 = (59-9)/5
5666 -> 5*(6+6)/6 = 5+6-6/6 = 66-56
5667 -> 5+6+6-7
＊5668 -> 8+[(6+6)/5] = 5*(8-\sqrt{6*6})
5669 -> 5*6/(9-6) =9+(6-5)^6 = 9+(6/6)^5
5677 -> 5+6-7/7 = 67-57
5678-> 5+6+7-8= (6*7+8)/5= (7*8-6)/5= 6+8/(7-5)= (7-5)*8-6= 5*((6+8)/7)= 8+(5+7)/6
5679-> 7+(9+6)/5 = 9+(6-5)^7 = 9+(7-6)^5
5688 -> 5+6-8/8 = 68-58
5689-> 5+6+8-9 = 9+(6-5)^8
5699 -> 5+6-9/9 = 9+(6-5)^9 = 69-59
5777 -> 5*(7+7)/7
5778 -> 7+(7+8)/5
5779 -> 5+7+7-9
＊5788 -> 7+[(8+8)/5] = 5*[(8+8)/7]
5789-> 7+9/(8-5)= (7-5)*9-8= 5*((7+9)/8)= (5*(7+9))/8= 8+(5+9)/7
＊5799 -> 5*(\sqrt{9*9}-7) = 5*[(9+9)/7]
5888 -> 5*(8+8)/8
＊5889 -> 9+[(5+8)/8] = 9+(8/8)^5 = 5*[(8+9)/8]
＊5899 -> 9+[(5+8)/9] = 9+[(5+9)/8] = 5*(8-\sqrt{9}-\sqrt{9}) = 9+(9-8)^5
5999 -> 5*(9+9)/9 = 9+(9/9)^5
＊6666 -> 6+6-[6/\sqrt{6}] = (66-6)/6
＊6667 -> 6+6-[6/\sqrt{7}] = 7+6-[\sqrt{6+7}] = 76-66
6668 -> 8+(6+6)/6
6669 -> 6+6*6/9 = (6*9+6)/6 = 9+(6/6)^9 = 9+9^{6-6}
＊6677 -> 7+7-6+[\sqrt{6}] = (67-7)/6 = (76-6)/7
6678 -> 7+6/(8-6) = 86-76
6679 -> 6+6+7-9 = 9+(7-6)^6 = 9+(6/6)^7 = 9+[(6+6)/7]
6688 -> (8-6)*8-6 = 8/(8-6) +6 = (86-6)/8 = (68-8)/6
6689 -> (9-6)*6-8 = 9+(6/6)^8 = 96-86 = 8+\sqrt{6*6/9}
6699 -> 6*(6+9)/9 = 9+(6/6)^9 = (96-6)/9 = (69-9)/6
＊6777 -> 7+6-[\sqrt{7+7}] = 7+7-6+[\sqrt{7}] = 77-67
＊6778 -> 8+[(7+7)/6]
6779 -> 7+6/(9-7) = 9+(7/7)^6
6788 -> (8*8+6)/7 = 8+(6+8)/7 = 78-68
6789-> 8/(9-7)+6= 6*(7+8)/9= (9-7)*8-6
6799 -> 7+9/(9-6) = 7+(9+9)/6 = 79-69 = 9+(7-6)^9
＊6888 -> 8+[(8+8)/6]
＊6889 -> 9+(8/8)^6 = 6+\sqrt{9}+8/8
＊6899 -> 9+(9-8)^6 = 8+6*\sqrt{9}/9
＊6999 -> 9+(9/9)^6 = 6+\sqrt{9}+9/9
＊7777 -> 7+7/7+[\sqrt{7}] = (77-7)/7
7778 -> 8+(7+7)/7 = 87-77
7779 -> (7+7*9)/7 = 9+(7/7)^7
＊7788 -> (78-8)/7 = (87-7)/8= 8+[(8+7)/7]
＊7789 -> 97-87 = 9+(7/7)^8 = 9+8-\sqrt{7*7} = 9+(8-7)^7
＊7799 -> (79-9)/7 = (97-7)/9= 9+(7/7)^9 = 9+[(7+7)/9]
＊7888 -> 8+[(8+8)/7] = 88-78
7889 -> 8+(7+9)/8 = 9+(8/8)^7 = 9+7^{8-8}
7899 -> (9-7)*9-8 = 89-79 = 9+(9-8)^7 = 8+[(8+9)/7]
＊7999 -> 9+(9/9)^7 = 9+[(7+9)/9]
8888 -> 8+(8+8)/8 = (88-8)/8
8889 -> (8*9+8)/8 =9+(8/8)^8=98-88
＊8899 -> (98-8)/9 = (89-9)/8= 9+(8/8)^9 = 9+9^{8-8} = 9+(9-8)^8 = 9+[(8+8)/9] = 8+[(9+9)/8]
8999 -> 8+(9+9)/9 = 9+(9/9)^8 = 9+8^{9-9} = 9+(9-8)^9 = 9+(9-8)^9 = 99-89
9999 -> (9*9+9)/9 =9+(9/9)^9=(99-9)/9
2013.6.27version
ミスプリントやここにないものを見つけた人はお知らせください。
10にするのではなく，1つの数の組み合わせから様々な数を作るという問題もあります．たとえば
5678では．
0を含む
すべて異なる