Solve {r}{68}{116}{123}{107}{81}{76}{90}{91}{95}{106}{99}{82}{77}{81}{111}{80}{98}{82}{56}{117}{98}{89}

$$\left. \begin{array} { r } { 68 } \\ { 116 } \\ { 123 } \\ { 107 } \\ { 81 } \\ { 76 } \\ { 90 } \\ { 91 } \\ { 95 } \\ { 106 } \\ { 99 } \\ { 82 } \\ { 77 } \\ { 81 } \\ { 111 } \\ { 80 } \\ { 98 } \\ { 82 } \\ { 56 } \\ { 117 } \\ { 98 } \\ { 89 } \end{array} \right.$$

Sort

$$56,68,76,77,80,81,81,82,82,89,90,91,95,98,98,99,106,107,111,116,117,123$$

Solution Steps

To sort the list, start from a single element 68.

$$68$$

Insert 116 to the appropriate location in the new list.

$$68,116$$

Insert 123 to the appropriate location in the new list.

$$68,116,123$$

Insert 107 to the appropriate location in the new list.

$$68,107,116,123$$

Insert 81 to the appropriate location in the new list.

$$68,81,107,116,123$$

Insert 76 to the appropriate location in the new list.

$$68,76,81,107,116,123$$

Insert 90 to the appropriate location in the new list.

$$68,76,81,90,107,116,123$$

Insert 91 to the appropriate location in the new list.

$$68,76,81,90,91,107,116,123$$

Insert 95 to the appropriate location in the new list.

$$68,76,81,90,91,95,107,116,123$$

Insert 106 to the appropriate location in the new list.

$$68,76,81,90,91,95,106,107,116,123$$

Insert 99 to the appropriate location in the new list.

$$68,76,81,90,91,95,99,106,107,116,123$$

Insert 82 to the appropriate location in the new list.

$$68,76,81,82,90,91,95,99,106,107,116,123$$

Insert 77 to the appropriate location in the new list.

$$68,76,77,81,82,90,91,95,99,106,107,116,123$$

Insert 81 to the appropriate location in the new list.

$$68,76,77,81,81,82,90,91,95,99,106,107,116,123$$

Insert 111 to the appropriate location in the new list.

$$68,76,77,81,81,82,90,91,95,99,106,107,111,116,123$$

Insert 80 to the appropriate location in the new list.

$$68,76,77,80,81,81,82,90,91,95,99,106,107,111,116,123$$

Insert 98 to the appropriate location in the new list.

$$68,76,77,80,81,81,82,90,91,95,98,99,106,107,111,116,123$$

Insert 82 to the appropriate location in the new list.

$$68,76,77,80,81,81,82,82,90,91,95,98,99,106,107,111,116,123$$

Insert 56 to the appropriate location in the new list.

$$56,68,76,77,80,81,81,82,82,90,91,95,98,99,106,107,111,116,123$$

Insert 117 to the appropriate location in the new list.

$$56,68,76,77,80,81,81,82,82,90,91,95,98,99,106,107,111,116,117,123$$

Insert 98 to the appropriate location in the new list.

$$56,68,76,77,80,81,81,82,82,90,91,95,98,98,99,106,107,111,116,117,123$$

Insert 89 to the appropriate location in the new list.

$$56,68,76,77,80,81,81,82,82,89,90,91,95,98,98,99,106,107,111,116,117,123$$

Evaluate

$$68,\ 116,\ 123,\ 107,\ 81,\ 76,\ 90,\ 91,\ 95,\ 106,\ 99,\ 82,\ 77,\ 81,\ 111,\ 80,\ 98,\ 82,\ 56,\ 117,\ 98,\ 89$$