Q:

Remove border-left from last cell in a table which is inside a parent table

I have a dynamically generated calendar which is made up of tables, each month in the main table is a cell and within this cell there is another table with cells for each day of the month.  
I need to grab the very last day cell in the entire table and remove its left border, not the last day cell for each month but the last day cell of the last month.  
Is it possible to do this css alone?  I have tried using last-child bit take the last day cell for every month which is not what I need. 
I have created a demo here to make it clear what I mean :  http://jsfiddle.net/9bXEp/
If you scroll right to the left you will see August 2014 and two rows below with the last cells containing 21 and T. If you look closely and inspect those cells you will see it has a border on the left which is causing a double border with the table's border.  Thats what I need to remove and I cannot direclty apply a class because in my application the tables are generated by php.  
Here is the code but jsfiddle will be much clearer
     <table class="main_table years">
    <tbody>
        <tr>
            <td class="main_table" style="vertical-align:text-top;">Resources</td>
            <td class="main_table years months">July, 2014</td>
            <td class="main_table years months">August, 2014</td>
        </tr>
        <tr>
            <td class="main_table years"></td>
            <td class="inner_container">
                <table class="main_table table_inner">
                    <tbody>
                        <tr>
                            <td class="no-b">
                                <div class="cell_width">30</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">31</div>
                            </td>
                        </tr>
                        <tr>
                            <td class="no-b2">
                                <div class="cell_width">W</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">T</div>
                            </td>
                        </tr>
                    </tbody>
                </table>
            </td>
            <td class="inner_container">
                <table class="main_table table_inner">
                    <tbody>
                        <tr>
                            <td class="no-b">
                                <div class="cell_width">1</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">2</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">3</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">4</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">5</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">6</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">7</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">8</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">9</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">10</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">11</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">12</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">13</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">14</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">15</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">16</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">17</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">18</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">19</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">20</div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width">21</div>
                            </td>
                        </tr>
                        <tr>
                            <td class="no-b2">
                                <div class="cell_width">F</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">S</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">S</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">M</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">T</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">W</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">T</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">F</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">S</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">S</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">M</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">T</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">W</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">T</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">F</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">S</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">S</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">M</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">T</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">W</div>
                            </td>
                            <td class="no-b2">
                                <div class="cell_width">T</div>
                            </td>
                        </tr>
                    </tbody>
                </table>
            </td>
        </tr>
        <tr id="7c0977ff-0ba1-2d74-b56d-52c4dff66cbd">
            <td class="cell_c link_c"><a href="index.php?module=Users&amp;action=DetailView&amp;record=7c0977ff-0ba1-2d74-b56d-52c4dff66cbd">guy</a>
            </td>
            <td colspan="2" class="no-b2">
                <table class="main_table table_inner" id="task0">
                    <tbody>
                        <tr>
                            <td class="no-b">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                        </tr>
                    </tbody>
                </table>
            </td>
        </tr>
        <tr id="1">
            <td class="cell_c link_c"><a href="index.php?module=Users&amp;action=DetailView&amp;record=1">Administrator</a>
            </td>
            <td colspan="2" class="no-b2">
                <table class="main_table table_inner" id="task1">
                    <tbody>
                        <tr>
                            <td class="no-b">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                            <td class="inner_td">
                                <div class="cell_width_chart day_block"></div>
                            </td>
                        </tr>
                    </tbody>
                </table>
            </td>
        </tr>
    </tbody>
</table>

A:

Use 
.inner_container:last-child tr:last-child .no-b2:last-child {
    border-left: none;
}

Which selects the last .inner_container, then the last tr (i.e. number row), then the last .no-b2 (i.e. day). 
Oh, and are you sure it's not border-right?