Teaser 2340: [Five girls]
From The Sunday Times, 29th July 2007 [link]
Five girls of different ages, 11 to 15, live in adjacent houses numbered 11 to 15, sit in different classrooms, 11 to 15, with different desk numbers, 11 to 15. Their ranked positions in class are different, too: 11 to 15. For each girl, these five numbers are different. Gina has house 14, classroom 11 and desk 13. Hilda came 13th in class and has desk 15. Iris’s classroom is 14. Jane, who is not [age] 13, has the same house number as Katy’s desk number.
What are Katy’s age, house number, classroom number, desk number and position?
This puzzle was originally published with no title.
[teaser2340]
Frits and 
NigelR are discussing. 
Ruud van der Ham, and 
Alex.T.Sutherland, 
Hugo, 
Jim Randell 9:29 am on 3 October 2026 Permalink |
Here is a solution using the [
SubstitutedExpression] solver from the enigma.py libraryIt allocates values 1..5 (representing 11..15) to each attribute for each girl.
It runs in 114ms. (Internal runtime of the generated code is 213µs).
And here is a short Python program to run the solver and prettify the output:
from enigma import (SubstitutedExpression, chunk, printf) # construct the solver p = SubstitutedExpression.from_file(["{dir}/teaser2340.run"]) # run the solver for s in p.solve(verbose=0): # output solution names = ["Gina", "Hilda", "Iris", "Jane", "Katy"] attrs = ["age", "house", "class", "desk", "pos"] for (name, ks) in zip(names, chunk("ABCDEFGHIJKLMNPQRSTUVWXYZ", 5)): printf("{name:6s} \\", name=name + ":") for (v, k) in zip(attrs, ks): printf("{v}={x} \\", x=s[k] + 10) printf() printf()Solution: For Katy: age = 11, house = 13, class = 15, desk = 12, position = 14th.
The complete table is:
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Frits 10:44 am on 3 October 2026 Permalink |
from itertools import permutations # check for different numbers per column check = lambda g: all(len(s := [x for x in r if x]) == len(set(s)) for r in zip(*g)) # age, house number, classroom number, desk number and position dgts = set(range(11, 16)) # define grid g = [[0] * 5 for _ in range(5)] # "Gina has house 14, classroom 11, desk 13 g[0][1:4] = [14, 11, 13] # "Hilda has position 13, desk 15" g[1][3:] = [15, 13] # "Iris has classroom 14" g[2][2] = 14 sols, orig = set(), [list(r) for r in g] # Gina for g[0][0], g[0][4] in permutations(dgts.difference(orig[0]), 2): # Hilda for g[1][0], g[1][1], g[1][2] in permutations(dgts.difference(orig[1]), 3): if not check(g): continue # Iris for g[2][0], g[2][1], g[2][3], g[2][4] \ in permutations(dgts.difference(orig[2]), 4): if not check(g): continue # Jane for g[3] in permutations(dgts, 5): # Jane is not [age] 13 if g[3][0] == 13 or not check(g): continue # Jane has the same house number as Katy's desk number g[4][3] = g[3][1] # Kate for g[4][0], g[4][1], g[4][2], g[4][4] \ in permutations(dgts - {g[4][3]}, 4): if not check(g): continue sols.add(tuple(g[4])) g[4] = orig[4] g[3] = orig[3] g[2] = orig[2] print("answer:", ' or '.join(str(x) for x in sols))LikeLike
Frits 11:10 am on 3 October 2026 Permalink |
from itertools import permutations # check for different numbers per column check = lambda g: all(len(s := [x for x in r if x]) == len(set(s)) for r in zip(*g)) dgts = set(range(11, 16)) # define constants (G, H, I, J, K), (a, h, c, d, p) = (0, 1, 2, 3, 4), (0, 1, 2, 3, 4) # define grid g = [[0] * 5 for _ in range(5)] # Gina has house 14, classroom 11, desk 13 g[G][1:4] = [14, 11, 13] # Hilda has position 13, desk 15 g[H][3:] = [15, 13] # Iris has classroom 14 g[I][c] = 14 sols, orig = set(), [list(r) for r in g] # Gina (choose age and house number) for g[G][a], g[G][p] in permutations(dgts.difference(orig[G]), 2): # Hilda (choose age, house number and classroom number) for g[H][a], g[H][h], g[H][c] in permutations(dgts.difference(orig[H]), 3): if not check(g): continue # Iris (choose age, house number, desk number and position) for g[I][a], g[I][h], g[I][d], g[I][p] \ in permutations(dgts.difference(orig[I]), 4): if not check(g): continue # Jane for g[J] in permutations(dgts, 5): # Jane has the same house number as Katy's desk number g[K][d] = g[J][h] # Jane is not [age] 13 if g[J][a] == 13 or not check(g): continue # Kate (choose age, house number, classroom number and position) for g[K][a], g[K][h], g[K][c], g[K][p] \ in permutations(dgts - {g[K][d]}, 4): if not check(g): continue sols.add(tuple(g[K])) g[K] = orig[K] g[J] = orig[J] g[I] = orig[I] print("answer:", ' or '.join(str(x) for x in sols))LikeLike
Frits 12:16 pm on 3 October 2026 Permalink |
Using constant variables instead of hardcoded digits slowed things down.
Calculating the numbers for Kate out of the remaining column values also seems to cause a higher run time.
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