The site's wording asks two things: for necessary and sufficient conditions for block-compatibility, and whether at least $\exp(cn^{1/2}\log n)$ sequences are block-compatible for all large $n$. The first has no yes-or-no answer: block-compatibility is itself a necessary and sufficient condition, and for each $n$ a finite search decides it, so, read as the site words it, it is trivially answered, and read as a request for a reasonable characterization it names no criterion for an answer. Erdős's own words set it apart from the problem. In [Er81], Part VI, item 2 (p. 12 of the copy; p. 35 of the journal), Erdős writes "One could ask: Give necessary and sufficient conditions for the $\{X_i\}$, that there should be a pairwise balanced block design $\{A_i\}$ satisfying $|A_i|=X_i$? Trivially we must have $\sum_{i=1}^m\binom{X_i}{2}=\binom{n}{2}$. Perhaps there will not be a reasonable necessary and sufficient condition. On the other hand the following problem should not be hopeless", and then states display (1), $\exp(c_1n^{1/2}\log n)<F(n)<\exp(c_2n^{1/2}\log n)$ for the number $F(n)$ of block-compatible sequences, adding that the upper bound is easy to prove and that Erdős had no success with the lower bound. The site reads the problem the same way: its label PROVED and its commentary credit Alon's lower bound $2^{(1/2+o(1))n^{1/2}\log n}$, record Erdős's doubt that a reasonable condition exists, and claim no characterization; its thread (two comments of 4 October 2026, none by the curator) adds nothing on the first question. Alon's Problem 4.2 in [Al26], which Alon identifies with Problem 732, states the counting question alone. The change removes the sentence "Are there necessary and sufficient conditions for $(X_i)$ to be block-compatible?" and inserts nothing; the site asks only the lower bound of Erdős's (1), and the upper bound, Erdős's and Alon's Section 4.3, is recorded in the Current assessment. The answer under the site's reading is yes, by Alon's Theorem 4.5 (Theorem 2.3 of the note), on the claim page. Under the reading the page does not adopt, the characterization question has no claimed answer: the sum condition is necessary and not sufficient (for $n=5$ the sizes $4,3,2$ satisfy it, but blocks of sizes $4$ and $3$ on five points share two points), and the sequences satisfying it alone far outnumber the block-compatible ones (Adenwalla's thread comment of 4 October 2026 gives their count as the coefficient of $x^{\binom n2}$ in $\prod_{i\ge2}(1-x^{\binom i2})^{-1}$, reportedly of order $n^{-3}\exp(cn^{2/3})$, against Erdős's upper bound $\exp(O(n^{1/2}\log n))$; a thread comment, credited and not relied on). That question stays in Formulation with no claim page. Results about the site's wording, credited and never counted: none; the formal-conjectures statement file and Jingxuan Ding's Lean development erdos732_yes (SpringSense Innovation Institute, commit c8c4bbbd13024e4ed45a0548c75c64664501e067, announced in the thread on 4 October 2026) both state the counting question, which is the precise Statement, and neither is built here. The page's standing judges the precise Statement.