Mate in 4 and 5

Logic Level 4

It is White's move. White can mate in 4 and in 5 starting with the same move. What is that move?

The bottom left corner square has coordinates ( 0 , 0 ) (0, 0) . Each piece has a value: Bishop = 3 \text{Bishop}=3 , Pawn = 1 \text{Pawn}=1 and King = 4 \text{King}=4 .

Submit your answer as V × x 1 × y 1 V\times { x }_{ 1 }\times { y }_{ 1 } , where V V denotes the value of the piece that White must move and the coordinates of the square where it has to go are ( x 1 , y 1 ) \left( { x }_{ 1 },{ y }_{ 1 } \right) .

Clarification: Black plays optimally .


This is the fourth problem of the set Mate .


The answer is 21.

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2 solutions

White can mate black in four moves even if he's playing optimally:

  1. Bh2 1...exd5

  2. g4+ 2...Ke6

  3. Be8 3... (whatever blak plays does not matter)

  4. f5#

Doesn't Be3 accomplish the same thing?

Eilon Lavi - 4 years, 5 months ago

1.Bh2 1...exd5

2.g4+ 2...Ke6

3.f5+ 3... Kd7

4.e6+ 4...Kc8

5.d7#

The answer is 3 × 7 × 1 = 21 3 \times 7 \times 1=\boxed{21} .

Motivation: Black King has no escape squares. We want to give checks with the g pawn because if we have to give it with the white bishop(bringing it back and giving a check in the b1-h7 diagonal), the king escapes via g4.

If we play g4, the f pawn becomes unsupported. Further, we see that once we support the f pawn, black has to play exd5. Using similar logic, we see that we have to support the pawn chain g3-f4-e5-d6.

Bh2 is the only move which does this.

Well done. Add the variant for mate in 4.

Mateo Matijasevick - 5 years, 1 month ago

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You may add it as you found it and deserve credit for it.

A Former Brilliant Member - 5 years, 1 month ago

cant it just check in one move tho?

NSCS 747 - 11 months, 1 week ago

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