In　the　combinatorial　context,　one　of　the　key　problems　in　sequence　reconstruction　is　to　find　the　largest　intersection　of　two　metric　balls　of　radius　r.　In　this　paper　we　study　this　problem　for　permutations　of　length　n　distorted　by　Hamming　errors　and　determine　the　size　of　the　largest　intersection　of　two　metric　balls　with　radius　r　whose　centers　are　at　distance　d=2,3,4\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$d=2,3,4$$\end{document}.　Moreover,　it　is　shown　that　for　any　n　＞=　3\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$n\geqslant　3$$\end{document}　an　arbitrary　permutation　is　uniquely　reconstructible　from　four　distinct　permutations　at　Hamming　distance　at　most　two　from　the　given　one,　and　it　is　proved　that　for　any　n　＞=　4\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$n\geqslant　4$$\end{document}　an　arbitrary　permutation　is　uniquely　reconstructible　from　4n-5\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$4n-5$$\end{document}　distinct　permutations　at　Hamming　distance　at　most　three　from　the　permutation.　It　is　also　proved　that　for　any　n　＞=　5\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$n\geqslant　5$$\end{document}　an　arbitrary　permutation　is　uniquely　reconstructible　from　7n2-31n+37\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$7n＜^＞2-31n+37$$\end{document}　distinct　permutations　at　Hamming　distance　at　most　four　from　the　permutation.　Finally,　in　the　case　of　at　most　r　Hamming　errors　and　sufficiently　large　n,　it　is　shown　that　at　least　Theta(nr-2)\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$${\varTheta　}(n＜^＞{r-2})$$\end{document}　distinct　erroneous　patterns　are　required　in　order　to　reconstruct　an　arbitrary　permutation.