将数字2至9填入8个圆圈中，使得每一行和每一列中的数字总和相等。将4个阴影圆圈中的数字相加。这4个数字之和的最大可能值是 ____。

1. 我做得对吗？
2. <details class="reasoning-details"> <summary style="cursor:pointer; color:#666; font-size:0.9em;">思考过程 (点击展开)</summary> <div class="reasoning-block"> **Analyzing the Discrepancy** I'm currently investigating a discrepancy where a student arrived at 29, but the correct answer is 28. My current focus is on understanding how the number of elements (2-9, totaling 8) and their sum (44) interact with the 2x2 grid and shaded circle configurations to produce this incorrect result. **Deriving the Constraint** I've pinpointed that the student's answer of 29 is incorrect because the sum of the shaded circles, M, must be a multiple of 4. This arises from the row and column sum relationships. I'm now focused on showing the student this divisibility constraint and guiding them towards finding the correct answer. </div> </details> 答案不是 29 哦，不过你能想到往大数凑很接近了！ 我们来看一下图形的结构约束： 图中有 2 行和 2 列，假设每行、每列的和都是 $S$。 如果把这 2 行和 2 列的和全部加起来（总共是 $4S$）： 1. 4 个白色圆圈各被加了几次？ 2. 4 个阴影圆圈各被加了几次？ 试着把 $4S$ 用「8 个数的总和」与「4 个阴影圆圈的和 $M$」表示出来，看看 $M$ 必须满足什么特殊的整除性质？