A Royal Tour of 15 by Agricola

Puzzle explanation

The puzzle’s theme was the Bridges of Königsberg problem: the question of whether it was possible to make a tour of the seven bridges over the river Pregel in the Prussian city of Königsberg, that crossed every bridge exactly once (and crossed the river in no other ways). The unclued entry at 15ac was KÖNIGSBERG and the corrections to misprints spelt BRIDGE. The extra letters in wordplay spelt EULER: Leonhard Euler proved that such a tour was impossible, using topological ideas and laying the foundations of graph theory. The letters omitted in wordplay spelt CAUCHY (Augustin-Louis Cauchy), who built on Euler’s ideas. The first letters of extra words in clues spelt “homotopic letters coloured alike”. Letters of the alphabet can be grouped according to their topology (in their standard forms): ADOPQR are the letters with one loop (they are topologically equivalent to a circle), B is the only one with two loops, and the rest have no loops. Colouring all occurrences of the homotopic (having the same topology) letters ADOPQR in one colour, the Bs in another and the rest in a third colour (eg white) produced a diagram of Königsberg’s river with the Bs representing the seven bridges. To make a non-repeating tour of all the bridges possible, the D in cell 14 was changed to B, a new bridge. (Entries were marked correct if the new B was shown in the bridge colour, the river colour or an obvious combination of both. Colouring of the cells, the letters or both was accepted.) Crossing this new bridge required a diagonal move, unlike the other crossings, which were all horizontal or vertical, so an entire tour would be possible only by using the moves of a king or queen (in chess).

Clue explanations

Conventions: * = anagram, < = reversal

No Extra word/(misprint) Answer (unclued letter) Explanation [extra letter]
Across
1   ENISLES E + NIS + LE[E]S
6   FELI(C)E BELIEF * − B
10   CENTUM T in NUM after C[U]E
11 humiliated EUNUCHS EU + (SHUN around C) <
12 outrageously TWI TWI(g)
13 maple BAOBAB BOA < in BAB(y)
14 odist DIT 2 meanings
18 teetotal PROPEL OPEL after PR
19 off PSORA (dro)PS OR A(bates)
20   YELP [L]YE + L(ongshi)P
22   B(A)BOON BB + OON
26 Press YELLED YELL + ED
27   (U)NIT TIN <
29 Italian EISEL (I SEE) * + L
32 (B)oat HARBOR H + ARBOR
34 condones LIFESTYLES (ELY ITSELF) * + S
35 Latin TEN NET <
36 Ems’s ILLITE IT in (ILL + E)
38 Dee(R) ELK (y)ELK
39 traffic UNSTEEL EEL after UNST
40 trophy HEEZIE H + homophone of EASY
41 eight MISSET (S + TIMES) *
42 relieve SENVIES SEN + VIES
Down
1   E(C)TOPY (du)E TO PY(aemia)
2   NEWER NEAR with WE[E] for A
3 squire’s STROPPY PP in STROY
4 cassava EMAIL LIANE < with M for N
5 obscure SEO OES <
6 leverage FUBSY (SB in YU + F) <
7 O(I)ls LUBES B in GLUES − G
8   C(H)IGRE CI-GÎT − IT + RE
9 only ESTRAY EST + YAR <
14   DROWN DOWN around R(ive)[R]
16 ugly NEBEL (o)NE BEL(gian)
17 bir(D) GIBLET GIB + LET
19 rabbits’ PODAL POD + A(dmits) L(uck)
21 electrode LYSIN LYN(x) around SI
23   NURE(Y)EV REVENU(e) *
24 dry MENTUM MEM around NUT *
25 (G)ods SILENI IN < after SILE
28 athlete TRIKES TIKES around R
30 liquid E-FITS EFTS around I
31 sk(E)rry ISLET I + S(ee) + LET(t)
32 III HYTHE H(enr)Y + THE
33 Keble OLLIE (c)OLLIE(r)
37 enjoy ILS (P)ILS
Back to 2024 menu