Grimshaw intersection

The classical chessmen (with the exception of knight and king) when examined in pairs, perform
Α. dissimilar linear movement, as in these pairs:
(1st) rook and bishop,
(2nd) rook and queen moving like a bishop,
(3rd) bishop and queen moving like a rook,
(4th) bishop and pawn making its first move with two steps
Β. similar linear move, as in these pairs:
(1st) rook and rook,
(2nd) rook and queen moving like a rook,
(3rd) bishop and queen moving like a bishop.


If the lines, on which move the two pieces that perform linear movement, have a common square, this square is called intersection.
If the first piece moves onto the free intersection, then it creates interference because it hinders the full action of the second piece. If the second piece, in another variation, can also go to the free intersection, then we observe mutual interference of the pieces.
We have various types of intersections. The Grimshaw intersection was first appeared in a chess problem of the composer Walter Grimshaw, and bears his name.

Theme: Grimshaw intersection : is the free square on which two black pieces with dissimilar linear movement are mutually interfered. Particularly the intersection with bishop and pawn is called pawn Grimshaw. White Grimshaw is the free square on which two white pieces with dissimilar linear movement are mutually interfered.

If we put a white piece on a Grimshaw intersection to force the black pieces (by taking the white) to mutually interfere, then the intersection is called Nowotny intersection.
For interferences of black pieces with similar linear movement, we will see Holzhauzen intersection (simple interference), and Wűrzburg-Plachutta intersection (mutual interference), and Plachutta intersection (placing of a white piece on the intersection to force mutual interference of the black pieces).

	(Problem 32) A. G. Corrias, ”Good Companion”, 1917 White plays and mates in 2 moves #2 (4+7)
[8/B2K3Q/5p2/3k4/2p2P2/p6p/r7/b7]

To make clear the theme of the Grimshaw intersection, we will study the solution of problem-32, by Corrias, with intersection of rook and bishop lines:

Key: 1.Qb1! [2.Qb7#] (Black has three ways of defense).
1...c3 (gives to the black king a new flight c4, but leaves d3 unguarded, allowing to white to give mate) 2.Qd3#
The other two defenses create thematic variations which present the theme Grimshaw intersection:
1...Bb2 (and the black bishop stops the white queen from reaching b7. But the bishop blocks one line of Ra2, which now can not reach g2 to stop the white from giving mate) 2.Qh1#
1...Rb2 (and the black rook stops the white queen from reaching b7. But the rook blocks one line of Ba1, which now can not reach e5 to stop the white from giving mate) 2.Qf5#

This mutual interference between two black pieces of dissimilar linear movement (here bishop and rook) on an intersection (the intersection here is the square b2) is the theme Grimshaw, which appears often enough in orthodox problems.

	(Problem 33) Frank Janet, ”St. Louis Globe Democrat”, 1916 White plays and mates in 2 moves #2 (6+8)
[6b1/2s1p2p/8/8/r4kSK/4Sp2/2B2P2/3Q1s2]

In problem-33, by Janet, we see a Grimshaw intersection between a pawn, which makes its two-step initial move, and a bishop:
Key: 1.Qd7! [2.Qf5#] (The black may answer by stopping the queen from reaching its destination square f5, but two of the black defenses have the fatal defect of the mutual interference of two black pieces).
1...Be6 (interferes with pawn e7, which can not move to e5, as defense for ...) 2.Qxc7#
1...e6 (interferes with Bg8, which can not move to c4, as defense for ...) 2.Qxa4#
This mutual interference between bishop and pawn on an intersection (here the intersection is the square e6) is the pawn Grimshaw.

The other (not thematic) variations of the problem are : 1...Se6 2.Sd5#, 1...Ra5 2.Qd4#, 1...Sxe3 2.fxe3#, 1...Sg3 2.fxg3# .

[This post in Greek language].