{ "id": "P078", "slug": "matrix-patterns", "key": "P078-matrix-patterns", "title": "Matrix patterns", "summary": "A grid filled in a clockwise spiral and read back along it, an odd magic square by the Siamese method with every row, column and diagonal sum checked, and the last grid turned and flipped - a magic square stays magic all eight ways.", "entry": "main.eml", "ui": "terminal", "readme": "# P078 - Matrix patterns\n\nA grid filled in a clockwise spiral and read back along it. An odd magic\nsquare made by the Siamese method, with every row, column and diagonal\nadded up. And the last grid turned and flipped: a magic square stays\nmagic all eight ways. It starts with the 3 x 3 magic square.\n\n- `main.eml` - the menu, reading sizes, showing grids and sums\n- `grids.eml` - blank grids, the spiral both ways, the magic square, the\n sums, the check, and the turns and flips\n\nHow each part works:\n\n- A grid is a list of rows, each made as its own list: repeating one row\n list would make every row the same list, so writing one square would\n change a whole column.\n- Spiral fill: 1, 2, 3, ... along the top edge, down the right, back\n along the bottom, up the left, then the four edges move in by one.\n- Spiral reading, as in the corpus case `spiral-matrix-traversal`, walks\n the same path. Two guards stop a last single row or column being read\n twice, which the 1 x 7 and 5 x 1 grids test.\n- Magic square, Siamese method, for an odd n: 1 goes in the middle of the\n top row. Each next number goes one up and one right, wrapping round the\n edges; if that square is taken, it goes one down instead. Every row,\n column and both diagonals then add up to n(n^2 + 1)/2: 15 for 3, 65 for\n 5, 175 for 7.\n- Turns and flips: a quarter turn clockwise, a mirror left to right, upside\n down, and a transpose (rows become columns). They move whole rows,\n columns and diagonals, so a magic square stays magic. Its 8 views are\n all different.\n\nWhat is checked: menu choices 1 to 5; 1 to 12 rows and columns for a\nspiral; an odd size from 3 to 15 for a magic square; turn, mirror, upside\ndown or transpose. An empty answer cancels.\n\nSessions: `sessions/basic.in` gives:\n- the 3 x 3 magic square, then spirals of 4 x 5, 1 x 7 and 5 x 1, each\n read back in order;\n- the 5 x 5 magic square with its sums, then turned, mirrored, transposed\n (back to the start) and turned upside down, magic each time;\n- the 7 x 7 magic square: every sum 175.\n\n`sessions/bad-input.in` gives:\n- menu choices 0 and x;\n- rows 0, 13 and abc, then a cancelled column count;\n- sizes 4, 17 and 1 for a magic square, then a cancel;\n- the move \"rotate\", then a cancel;\n- a 3 x 3 spiral turned: not a magic square.\n\nBuilt on the verified corpus case `spiral-matrix-traversal` (four\nshrinking edges, with the guards that stop a last row or column being\nread twice).\n", "modules": [ { "name": "main.eml", "eml": "# P078 matrix patterns: a grid filled in a spiral and read back, an odd\n# magic square by the Siamese method with all its sums, and the last grid\n# turned and flipped - a magic square stays magic all eight ways.\nimport grids\n\ndef trim(s):\n 0 => i\n len(s) => j\n while i < j and s[i] == \" \":\n i + 1 => i\n while j > i and s[j - 1] == \" \":\n j - 1 => j\n return s[i:j]\n\ndef number(s):\n if len(s) == 0 or len(s) > 2:\n return -1\n 0 => n\n for c in s:\n if not (c >= \"0\" and c <= \"9\"):\n return -1\n n * 10 + int(c) => n\n return n\n\ndef lpad(s, n):\n while len(s) < n:\n \" \" + s => s\n return s\n\ndef ask(prompt, low, high):\n while True:\n trim(input(prompt + \" (\" + str(low) + \" to \" + str(high) + \")> \")) => a\n if a == \"\":\n return -1\n number(a) => n\n if n >= low and n <= high:\n return n\n (\"Type a whole number from \" + str(low) + \" to \" + str(high) + \".\") ^0\n\ndef show(g):\n # Every column as wide as the widest number in the grid, plus a space.\n 1 => w\n for row in g:\n for x in row:\n if len(str(x)) > w:\n len(str(x)) => w\n for row in g:\n \"\" => line\n for x in row:\n line + lpad(str(x), w + 1) => line\n line ^0\n\ndef joined(xs):\n \"\" => s\n for x in xs:\n if s != \"\":\n s + \" \" => s\n s + str(x) => s\n return s\n\ndef spiral(g):\n ask(\"rows\", 1, 12) => r\n if r == -1:\n \"Cancelled.\" ^0\n return g\n ask(\"columns\", 1, 12) => c\n if c == -1:\n \"Cancelled.\" ^0\n return g\n grids.spiral_fill(r, c) => g\n show(g)\n grids.spiral_order(g) => path\n True => inorder\n for k in [0:len(path) - 1]:\n if path[k] != k + 1:\n False => inorder\n if inorder:\n (\"Read back along the same spiral: 1 to \" + str(r * c) + \" in order, each once.\") ^0\n else:\n (\"Read back along the same spiral: \" + joined(path)) ^0\n return g\n\ndef square(g):\n while True:\n trim(input(\"odd size (3 to 15)> \")) => a\n if a == \"\":\n \"Cancelled.\" ^0\n return g\n number(a) => n\n if n >= 3 and n <= 15 and n % 2 == 1:\n grids.magic(n) => g\n show(g)\n report(g)\n return g\n \"Type an odd whole number from 3 to 15.\" ^0\n\ndef report(g):\n len(g) => n\n grids.sums(g) => s\n (\"rows \" + joined(s[0])) ^0\n (\"columns \" + joined(s[1])) ^0\n (\"diagonals \" + str(s[2]) + \" and \" + str(s[3])) ^0\n int(n * (n * n + 1) / 2) => target\n if grids.is_magic(g):\n (\"Every row, column and both diagonals add up to \" + str(target) + \" = n(n^2 + 1)/2, with 1 to \" + str(n * n) + \" each once: magic.\") ^0\n else:\n (\"Not magic: n(n^2 + 1)/2 = \" + str(target) + \" is not every sum, or a number is missing.\") ^0\n\ndef move(g):\n while True:\n trim(input(\"turn, mirror, upside down or transpose> \")) => how\n if how == \"\":\n \"Cancelled.\" ^0\n return g\n if how == \"turn\" or how == \"mirror\" or how == \"upside down\" or how == \"transpose\":\n if how == \"turn\":\n grids.turned(g) => g\n elif how == \"mirror\":\n grids.mirrored(g) => g\n elif how == \"upside down\":\n grids.upside_down(g) => g\n else:\n grids.transposed(g) => g\n show(g)\n if len(g) == len(g[0]) and len(g) >= 3 and len(g) % 2 == 1:\n if grids.is_magic(g):\n \"Still magic: turning and flipping move whole rows, columns and diagonals.\" ^0\n else:\n \"Not a magic square - and turning or flipping cannot make one.\" ^0\n return g\n \"Type turn, mirror, upside down or transpose.\" ^0\n\ngrids.magic(3) => grid\n\n\"== Matrix patterns ==\" ^0\n\"Spirals, magic squares, and grids turned and flipped.\" ^0\nTrue => running\nwhile running:\n \"\" ^0\n \"1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\" ^0\n trim(input(\"choice> \")) => choice\n if choice == \"1\":\n spiral(grid) => grid\n elif choice == \"2\":\n square(grid) => grid\n elif choice == \"3\":\n move(grid) => grid\n elif choice == \"4\":\n show(grid)\n elif choice == \"5\":\n False => running\n else:\n \"Pick a number from 1 to 5.\" ^0\n\"Bye.\" ^0\n", "python": "import grids\n\ndef trim(s):\n i = 0\n j = len(s)\n while i < j and s[i] == \" \":\n i = i + 1\n while j > i and s[j - 1] == \" \":\n j = j - 1\n return s[i:j]\n\ndef number(s):\n if len(s) == 0 or len(s) > 2:\n return -1\n n = 0\n for c in s:\n if not (c >= \"0\" and c <= \"9\"):\n return -1\n n = n * 10 + int(c)\n return n\n\ndef lpad(s, n):\n while len(s) < n:\n s = \" \" + s\n return s\n\ndef ask(prompt, low, high):\n while True:\n a = trim(input(prompt + \" (\" + str(low) + \" to \" + str(high) + \")> \"))\n if a == \"\":\n return -1\n n = number(a)\n if n >= low and n <= high:\n return n\n print(\"Type a whole number from \" + str(low) + \" to \" + str(high) + \".\")\n\ndef show(g):\n w = 1\n for row in g:\n for x in row:\n if len(str(x)) > w:\n w = len(str(x))\n for row in g:\n line = \"\"\n for x in row:\n line = line + lpad(str(x), w + 1)\n print(line)\n\ndef joined(xs):\n s = \"\"\n for x in xs:\n if s != \"\":\n s = s + \" \"\n s = s + str(x)\n return s\n\ndef spiral(g):\n r = ask(\"rows\", 1, 12)\n if r == -1:\n print(\"Cancelled.\")\n return g\n c = ask(\"columns\", 1, 12)\n if c == -1:\n print(\"Cancelled.\")\n return g\n g = grids.spiral_fill(r, c)\n show(g)\n path = grids.spiral_order(g)\n inorder = True\n for k in range(0, len(path)):\n if path[k] != k + 1:\n inorder = False\n if inorder:\n print(\"Read back along the same spiral: 1 to \" + str(r * c) + \" in order, each once.\")\n else:\n print(\"Read back along the same spiral: \" + joined(path))\n return g\n\ndef square(g):\n while True:\n a = trim(input(\"odd size (3 to 15)> \"))\n if a == \"\":\n print(\"Cancelled.\")\n return g\n n = number(a)\n if n >= 3 and n <= 15 and n % 2 == 1:\n g = grids.magic(n)\n show(g)\n report(g)\n return g\n print(\"Type an odd whole number from 3 to 15.\")\n\ndef report(g):\n n = len(g)\n s = grids.sums(g)\n print(\"rows \" + joined(s[0]))\n print(\"columns \" + joined(s[1]))\n print(\"diagonals \" + str(s[2]) + \" and \" + str(s[3]))\n target = int(n * (n * n + 1) / 2)\n if grids.is_magic(g):\n print(\"Every row, column and both diagonals add up to \" + str(target) + \" = n(n^2 + 1)/2, with 1 to \" + str(n * n) + \" each once: magic.\")\n else:\n print(\"Not magic: n(n^2 + 1)/2 = \" + str(target) + \" is not every sum, or a number is missing.\")\n\ndef move(g):\n while True:\n how = trim(input(\"turn, mirror, upside down or transpose> \"))\n if how == \"\":\n print(\"Cancelled.\")\n return g\n if how == \"turn\" or how == \"mirror\" or how == \"upside down\" or how == \"transpose\":\n if how == \"turn\":\n g = grids.turned(g)\n elif how == \"mirror\":\n g = grids.mirrored(g)\n elif how == \"upside down\":\n g = grids.upside_down(g)\n else:\n g = grids.transposed(g)\n show(g)\n if len(g) == len(g[0]) and len(g) >= 3 and len(g) % 2 == 1:\n if grids.is_magic(g):\n print(\"Still magic: turning and flipping move whole rows, columns and diagonals.\")\n else:\n print(\"Not a magic square - and turning or flipping cannot make one.\")\n return g\n print(\"Type turn, mirror, upside down or transpose.\")\n\ngrid = grids.magic(3)\nprint(\"== Matrix patterns ==\")\nprint(\"Spirals, magic squares, and grids turned and flipped.\")\nrunning = True\nwhile running:\n print(\"\")\n print(\"1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\")\n choice = trim(input(\"choice> \"))\n if choice == \"1\":\n grid = spiral(grid)\n elif choice == \"2\":\n grid = square(grid)\n elif choice == \"3\":\n grid = move(grid)\n elif choice == \"4\":\n show(grid)\n elif choice == \"5\":\n running = False\n else:\n print(\"Pick a number from 1 to 5.\")\nprint(\"Bye.\")\n" }, { "name": "grids.eml", "eml": "# P078 matrix patterns - a grid filled in a spiral and read back the same\n# way, an odd magic square by the Siamese method with every sum checked,\n# and the grid turned and flipped. A grid is a list of rows.\n\ndef blank(rows, cols):\n # A rows x cols grid of zeros, each row its own list ([[0] * cols] *\n # rows would make every row the same list).\n [0] * rows => g\n for r in [0:rows - 1]:\n [0] * cols => g[r]\n return g\n\ndef spiral_fill(rows, cols):\n # 1, 2, 3, ... clockwise from the top left, turning inwards: along the\n # top edge, down the right, back along the bottom, up the left, and the\n # four edges move in by one.\n blank(rows, cols) => g\n 1 => n\n 0 => top\n rows - 1 => bottom\n 0 => left\n cols - 1 => right\n while top <= bottom and left <= right:\n for c in [left:right]:\n n => g[top][c]\n n + 1 => n\n top + 1 => top\n for r in [top:bottom]:\n n => g[r][right]\n n + 1 => n\n right - 1 => right\n if top <= bottom:\n for k in [0:right - left]:\n n => g[bottom][right - k]\n n + 1 => n\n bottom - 1 => bottom\n if left <= right:\n for k in [0:bottom - top]:\n n => g[bottom - k][left]\n n + 1 => n\n left + 1 => left\n return g\n\ndef spiral_order(g):\n # The corpus case spiral-matrix-traversal: read the same path. The two\n # guards stop a last single row or column being read twice.\n len(g) => rows\n len(g[0]) => cols\n [] => out\n 0 => top\n rows - 1 => bottom\n 0 => left\n cols - 1 => right\n while top <= bottom and left <= right:\n for c in [left:right]:\n out + [g[top][c]] => out\n top + 1 => top\n for r in [top:bottom]:\n out + [g[r][right]] => out\n right - 1 => right\n if top <= bottom:\n for k in [0:right - left]:\n out + [g[bottom][right - k]] => out\n bottom - 1 => bottom\n if left <= right:\n for k in [0:bottom - top]:\n out + [g[bottom - k][left]] => out\n left + 1 => left\n return out\n\ndef magic(n):\n # The Siamese method for an odd n: 1 in the middle of the top row, then\n # each next number one up and one right, wrapping round the edges; if\n # that square is taken, one down instead.\n blank(n, n) => g\n 0 => r\n int((n - 1) / 2) => c\n for k in [1:n * n]:\n k => g[r][c]\n (r - 1 + n) % n => up\n (c + 1) % n => over\n if g[up][over] != 0:\n (r + 1) % n => r\n else:\n up => r\n over => c\n return g\n\ndef sums(g):\n # [row sums, column sums, main diagonal, other diagonal].\n len(g) => n\n [0] * n => rs\n [0] * n => cs\n 0 => d1\n 0 => d2\n for r in [0:n - 1]:\n for c in [0:n - 1]:\n rs[r] + g[r][c] => rs[r]\n cs[c] + g[r][c] => cs[c]\n d1 + g[r][r] => d1\n d2 + g[r][n - 1 - r] => d2\n return [rs, cs, d1, d2]\n\ndef is_magic(g):\n # Every row, column and both diagonals add up to n(n^2 + 1)/2, and the\n # numbers are 1 to n^2 once each.\n len(g) => n\n int(n * (n * n + 1) / 2) => target\n sums(g) => s\n for x in s[0] + s[1] + [s[2], s[3]]:\n if x != target:\n return False\n [0] * (n * n + 1) => seen\n for row in g:\n for x in row:\n if x < 1 or x > n * n or seen[x] == 1:\n return False\n 1 => seen[x]\n return True\n\ndef turned(g):\n # A quarter turn clockwise: row r becomes column (rows - 1 - r).\n len(g) => rows\n len(g[0]) => cols\n blank(cols, rows) => out\n for r in [0:rows - 1]:\n for c in [0:cols - 1]:\n g[r][c] => out[c][rows - 1 - r]\n return out\n\ndef mirrored(g):\n # Flipped left to right.\n len(g) => rows\n len(g[0]) => cols\n blank(rows, cols) => out\n for r in [0:rows - 1]:\n for c in [0:cols - 1]:\n g[r][c] => out[r][cols - 1 - c]\n return out\n\ndef upside_down(g):\n # Flipped top to bottom.\n len(g) => rows\n blank(rows, len(g[0])) => out\n for r in [0:rows - 1]:\n for c in [0:len(g[0]) - 1]:\n g[r][c] => out[rows - 1 - r][c]\n return out\n\ndef transposed(g):\n # Rows become columns: flipped over the main diagonal.\n blank(len(g[0]), len(g)) => out\n for r in [0:len(g) - 1]:\n for c in [0:len(g[0]) - 1]:\n g[r][c] => out[c][r]\n return out\n", "python": "def blank(rows, cols):\n g = [0] * rows\n for r in range(0, rows):\n g[r] = [0] * cols\n return g\n\ndef spiral_fill(rows, cols):\n g = blank(rows, cols)\n n = 1\n top = 0\n bottom = rows - 1\n left = 0\n right = cols - 1\n while top <= bottom and left <= right:\n for c in range(left, right+1):\n g[top][c] = n\n n = n + 1\n top = top + 1\n for r in range(top, bottom+1):\n g[r][right] = n\n n = n + 1\n right = right - 1\n if top <= bottom:\n for k in range(0, right - left+1):\n g[bottom][right - k] = n\n n = n + 1\n bottom = bottom - 1\n if left <= right:\n for k in range(0, bottom - top+1):\n g[bottom - k][left] = n\n n = n + 1\n left = left + 1\n return g\n\ndef spiral_order(g):\n rows = len(g)\n cols = len(g[0])\n out = []\n top = 0\n bottom = rows - 1\n left = 0\n right = cols - 1\n while top <= bottom and left <= right:\n for c in range(left, right+1):\n out = out + [g[top][c]]\n top = top + 1\n for r in range(top, bottom+1):\n out = out + [g[r][right]]\n right = right - 1\n if top <= bottom:\n for k in range(0, right - left+1):\n out = out + [g[bottom][right - k]]\n bottom = bottom - 1\n if left <= right:\n for k in range(0, bottom - top+1):\n out = out + [g[bottom - k][left]]\n left = left + 1\n return out\n\ndef magic(n):\n g = blank(n, n)\n r = 0\n c = int((n - 1) / 2)\n for k in range(1, n * n+1):\n g[r][c] = k\n up = (r - 1 + n) % n\n over = (c + 1) % n\n if g[up][over] != 0:\n r = (r + 1) % n\n else:\n r = up\n c = over\n return g\n\ndef sums(g):\n n = len(g)\n rs = [0] * n\n cs = [0] * n\n d1 = 0\n d2 = 0\n for r in range(0, n):\n for c in range(0, n):\n rs[r] = rs[r] + g[r][c]\n cs[c] = cs[c] + g[r][c]\n d1 = d1 + g[r][r]\n d2 = d2 + g[r][n - 1 - r]\n return [rs, cs, d1, d2]\n\ndef is_magic(g):\n n = len(g)\n target = int(n * (n * n + 1) / 2)\n s = sums(g)\n for x in s[0] + s[1] + [s[2], s[3]]:\n if x != target:\n return False\n seen = [0] * (n * n + 1)\n for row in g:\n for x in row:\n if x < 1 or x > n * n or seen[x] == 1:\n return False\n seen[x] = 1\n return True\n\ndef turned(g):\n rows = len(g)\n cols = len(g[0])\n out = blank(cols, rows)\n for r in range(0, rows):\n for c in range(0, cols):\n out[c][rows - 1 - r] = g[r][c]\n return out\n\ndef mirrored(g):\n rows = len(g)\n cols = len(g[0])\n out = blank(rows, cols)\n for r in range(0, rows):\n for c in range(0, cols):\n out[r][cols - 1 - c] = g[r][c]\n return out\n\ndef upside_down(g):\n rows = len(g)\n out = blank(rows, len(g[0]))\n for r in range(0, rows):\n for c in range(0, len(g[0])):\n out[rows - 1 - r][c] = g[r][c]\n return out\n\ndef transposed(g):\n out = blank(len(g[0]), len(g))\n for r in range(0, len(g)):\n for c in range(0, len(g[0])):\n out[c][r] = g[r][c]\n return out\n" } ], "sessions": [ { "name": "bad-input", "input": "0\nx\n1\n0\n13\nabc\n3\n\n2\n4\n17\n1\n\n3\nrotate\n\n1\n3\n3\n3\nturn\n5\n", "screen": "== Matrix patterns ==\nSpirals, magic squares, and grids turned and flipped.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 0\nPick a number from 1 to 5.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> x\nPick a number from 1 to 5.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 1\nrows (1 to 12)> 0\nType a whole number from 1 to 12.\nrows (1 to 12)> 13\nType a whole number from 1 to 12.\nrows (1 to 12)> abc\nType a whole number from 1 to 12.\nrows (1 to 12)> 3\ncolumns (1 to 12)> \nCancelled.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 2\nodd size (3 to 15)> 4\nType an odd whole number from 3 to 15.\nodd size (3 to 15)> 17\nType an odd whole number from 3 to 15.\nodd size (3 to 15)> 1\nType an odd whole number from 3 to 15.\nodd size (3 to 15)> \nCancelled.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 3\nturn, mirror, upside down or transpose> rotate\nType turn, mirror, upside down or transpose.\nturn, mirror, upside down or transpose> \nCancelled.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 1\nrows (1 to 12)> 3\ncolumns (1 to 12)> 3\n 1 2 3\n 8 9 4\n 7 6 5\nRead back along the same spiral: 1 to 9 in order, each once.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 3\nturn, mirror, upside down or transpose> turn\n 7 8 1\n 6 9 2\n 5 4 3\nNot a magic square - and turning or flipping cannot make one.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 5\nBye.\n", "interpreter": "equal" }, { "name": "basic", "input": "4\n1\n4\n5\n1\n1\n7\n1\n5\n1\n2\n5\n3\nturn\n3\nmirror\n3\ntranspose\n3\nupside down\n2\n7\n5\n", "screen": "== Matrix patterns ==\nSpirals, magic squares, and grids turned and flipped.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 4\n 8 1 6\n 3 5 7\n 4 9 2\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 1\nrows (1 to 12)> 4\ncolumns (1 to 12)> 5\n 1 2 3 4 5\n 14 15 16 17 6\n 13 20 19 18 7\n 12 11 10 9 8\nRead back along the same spiral: 1 to 20 in order, each once.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 1\nrows (1 to 12)> 1\ncolumns (1 to 12)> 7\n 1 2 3 4 5 6 7\nRead back along the same spiral: 1 to 7 in order, each once.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 1\nrows (1 to 12)> 5\ncolumns (1 to 12)> 1\n 1\n 2\n 3\n 4\n 5\nRead back along the same spiral: 1 to 5 in order, each once.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 2\nodd size (3 to 15)> 5\n 17 24 1 8 15\n 23 5 7 14 16\n 4 6 13 20 22\n 10 12 19 21 3\n 11 18 25 2 9\nrows 65 65 65 65 65\ncolumns 65 65 65 65 65\ndiagonals 65 and 65\nEvery row, column and both diagonals add up to 65 = n(n^2 + 1)/2, with 1 to 25 each once: magic.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 3\nturn, mirror, upside down or transpose> turn\n 11 10 4 23 17\n 18 12 6 5 24\n 25 19 13 7 1\n 2 21 20 14 8\n 9 3 22 16 15\nStill magic: turning and flipping move whole rows, columns and diagonals.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 3\nturn, mirror, upside down or transpose> mirror\n 17 23 4 10 11\n 24 5 6 12 18\n 1 7 13 19 25\n 8 14 20 21 2\n 15 16 22 3 9\nStill magic: turning and flipping move whole rows, columns and diagonals.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 3\nturn, mirror, upside down or transpose> transpose\n 17 24 1 8 15\n 23 5 7 14 16\n 4 6 13 20 22\n 10 12 19 21 3\n 11 18 25 2 9\nStill magic: turning and flipping move whole rows, columns and diagonals.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 3\nturn, mirror, upside down or transpose> upside down\n 11 18 25 2 9\n 10 12 19 21 3\n 4 6 13 20 22\n 23 5 7 14 16\n 17 24 1 8 15\nStill magic: turning and flipping move whole rows, columns and diagonals.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 2\nodd size (3 to 15)> 7\n 30 39 48 1 10 19 28\n 38 47 7 9 18 27 29\n 46 6 8 17 26 35 37\n 5 14 16 25 34 36 45\n 13 15 24 33 42 44 4\n 21 23 32 41 43 3 12\n 22 31 40 49 2 11 20\nrows 175 175 175 175 175 175 175\ncolumns 175 175 175 175 175 175 175\ndiagonals 175 and 175\nEvery row, column and both diagonals add up to 175 = n(n^2 + 1)/2, with 1 to 49 each once: magic.\n\n1) spiral 2) magic square 3) turn or flip the last grid 4) show it 5) quit\nchoice> 5\nBye.\n", "interpreter": "equal" } ], "builtOn": [ { "slug": "spiral-matrix-traversal", "caseId": "104-spiral-matrix-traversal", "title": "Spiral matrix traversal" } ], "updated": "2026-10-14" }