Mathematical_Recreations-Kraitchik-2e

Game8 275
(16 moves for the 8 pawns and 4 moves for the 2 knights).
Black can answer in any of 20 different ways for each move
of White. Thus there are 20·20 = 400 different ways in
which the first moves on each side can be made.
In general the number of possible moves increases after
a
o 1 2 3 4 5 6 7
o 0 312 ~ 36 ~ 36 424 5 lGO
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1 312 ~ h ~ Sa 428 33 416
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2 ~ it 454 39 21 36 418 505
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b 3 36 ~ 39 22 Sa 424 31 412
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4 ~ Sa 21 33 432 Sa 412 560
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5 Sa ~ Sa 424 33 4s 585 44
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6 424 33 -its 31 412 585 46 525
---------------------
7 5100 416 595 412 560 44 525 6238
. FIGURE 148. Knight's Move.
the first. For example, 'Vhite's second move can be made
in 29 different ways if his first move was P to K4, in 30 ways
if it was P to K3. Later in the game the number of possibilities
increases enormously. If the queen is on Q5, she alone
has 27 possible moves (if the cells where the moves end are
free and accessible).