If two different numbers are randomly selected from the 100 natural numbers 1, 2, 3, 4, ..., 100, so that the sum of the two numbers is a multiple of 6, how many different methods are there?
在1，2，3，4，…，100这100个自然数中任取两个不同的数，使得取出的两数之和是6的倍数，则有多少种不同的取法？
<gadget id="calculator">17 * 16</gadget>
<output>272</output>

<gadget id="calculator">17 * 17</gadget>
<output>289</output>

<gadget id="calculator">16 / 2</gadget>
<output>8</output>

<gadget id="calculator">17 * 8</gadget>
<output>136</output>

<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">16 * (15/2)</gadget>
<output>120</output>

<gadget id="calculator">272 + 289 + 136 + 120</gadget>
<output>817</output>

<result>817</result>