Assume that among four groups of four different positive integers, the sum of the smallest number and the average of the remaining three numbers is 17, and the sum of the average of the largest number and the remaining three numbers is 29. In the four arrays that satisfy the above conditions, what is the maximum value of the largest number.
设四个不同的正整数构成的四数组中，最小的数与其余三数的平均值之和为17，而最大的数与其余三数的平均值之和为29．在满足上述条件的四数组中，其最大数的最大值是多少．
<gadget id="calculator">18 + 5</gadget>
<output>23</output>

<result>23</result>