Subtract-a-square (also referred to as take-a-square) is a two-player mathematical subtraction game. It is played by two people with a pile of coins (or other tokens) between them. The players take turns removing coins from the pile, always removing a non-zero square number of coins. The game is usually played as a normal play game, which means that the player who removes the last coin wins.[1][2] It is an impartial game, meaning that the set of moves available from any position does not depend on whose turn it is. Solomon W. Golomb credits the invention of this game to Richard A. Epstein.[3]
^Silverman, David L. (1971), "61. Subtract-a-square", Your Move: Logic, Math and Word Puzzles for Enthusiasts, Dover Publications, p. 143, ISBN 9780486267319
^Dunn, Angela (1980), "Subtract-a-square", Mathematical Bafflers, Dover Publications, p. 102, ISBN 9780486239613
^Golomb, Solomon W. (1966), "A mathematical investigation of games of "take-away"", Journal of Combinatorial Theory, 1 (4): 443–458, doi:10.1016/S0021-9800(66)80016-9, MR 0209015.
Subtract-a-square (also referred to as take-a-square) is a two-player mathematical subtraction game. It is played by two people with a pile of coins (or...
Units (SI) with symbol m2. It is the area of asquare with sides one metre in length. Adding and subtracting SI prefixes creates multiples and submultiples;...
Impartial games include Nim, Sprouts, Kayles, Quarto, Cram, Chomp, Subtractasquare, Notakto, and poset games. Go and chess are not impartial, as each...
magic squares. Self-complementary magic square when it is a magic square which when complemented (i.e. each number subtracted from n2 + 1) will give a rotated...
Subtractive synthesis is a method of sound synthesis in which partials of an audio signal (often one rich in harmonics) are attenuated by a filter to...
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difference of two squares is asquared (multiplied by itself) number subtracted from another squared number. Every difference of squares may be factored...
pandiagonal magic squarea 11 a 12 a 13 a 14 a 15 a 21 a 22 a 23 a 24 a 25 a 31 a 32 a 33 a 34 a 35 a 41 a 42 a 43 a 44 a 45 a 51 a 52 a 53 a 54 a 55 {\displaystyle...
number as a 32-bit integer, a logical shift right by one bit is performed and the result subtracted from the number 0x5F3759DF, which is a floating-point...
Alternatively, the nth square number can be calculated from the previous two by doubling the (n − 1)th square, subtracting the (n − 2)th square number, and adding...
playing only with a single pile of tokens, optimal play is trivial (simply remove all the tokens in a single move). Subtractasquare is a variation of nim...
Square wave sound sample 5 seconds of square wave at 220 Hz Problems playing this file? See media help. Asquare wave is a non-sinusoidal periodic waveform...
trick of pre-subtracting the square of the previous digits which makes a general multiplication step unnecessary. See Methods of computing square roots § Binary...
the two digits of the square you just brought down. Thus the next p will be the old p times 10 plus x. Subtract y from c to form a new remainder. If the...
than 50 (n = 50 + a), add 100×a instead of subtracting it. This method requires the memorization of squares from 1 to 24. The square of n (most easily...
Stein, Flight of the Vin Fiz, Arbor House, 1985, ISBN 0-87795-672-3. Subtractasquare, a mathematical game invented by Epstein "Contributors". IEEE Transactions...
999999 If you square the last three digits and subtract the square of the first three digits, you also get back a cyclic permutation of the number.[citation...
statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with...
processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure...
numbers, and for many years he had known how to add and subtract triples of numbers. However, for a long time, he had been stuck on the problem of multiplication...
because a {\displaystyle a} is non-zero. Afterwards, we subtract the constant term c / a {\displaystyle c/a} to isolate it on the right-hand side: a x 2 |...
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