# 
# Written by:
# -- 
# John L. Weatherwax                2007-07-05
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

# Jousting in a Tournament:
# 
tournament_number = 1:11
numbers_less_than = tournament_number - 1
numbers_greater_than = 11 - tournament_number
number_product = numbers_less_than * numbers_greater_than
rbind( tournament_number, numbers_less_than, numbers_greater_than, number_product )


# How much for a Knife, Sword, or Arrow:
# 
arrows = 1:floor( 72/22 )
knives = ( 72 - 22 * arrows ) / 3 
rbind( arrows, knives )


# What is the Human Population of South Primm:
# 
N = 420
sum( c( 1/3, 1/4, 1/5, 1/7 ) * N )


# Strange Rabbits:
# 
x = -20:+20
y = ( 13 - 5 * x ) / 7
integer_y = y == as.integer(y)

int_x = x[ integer_y ]
int_y = y[ integer_y ]
num_jumps = abs(int_x) + abs(int_y) 
R = rbind( int_x, int_y, num_jumps )
rownames(R) = c("X","Y","Num. Jumps")
print(R)


# Minotaur Fighters:
# 
A = matrix( data=c(4,-4,-4, -2,6,-2, -1,-1,7), nrow=3, ncol=3, byrow=TRUE )
b = matrix( data=c(48,48,48), nrow=3 )
solve(A, b)


print("Switching Allegiance:")
# 
Ls = 5:13
Ms = 7:15
print( rbind( Ls, Ms, Ms+1, Ls-1 ) )



print("Able and Gallant Soldiers:")
# 
A = matrix( data=c(1,1,1,1, -1,0,0,1, 1,1,-1,-1, 0,1,0,-1), nrow=4, ncol=4, byrow=TRUE )
b = matrix( data=c(50,0,-2,-4), nrow=4 )
x = solve(A, b)
print(A)
print(t(b))
print(t(x))

print("How Many Eggs?")
#
eggs = 5:39
M = rbind( eggs, eggs %% 2 - 1, eggs %% 3, eggs %% 5 - 3 )
rownames(M) = c("eggs", "mod 2 - 1", "mod 3", "mod 5 - 3" )
print(M)



print("Daughters of Alexis")
#
M = matrix( data=c(1,1,9, 1,2,8, 1,3,7, 1,4,6, 1,5,5, 2,2,7, 2,3,6, 2,4,5, 3,3,5, 3,4,4), ncol=3, byrow=TRUE )
print( M )
print( rowSums(M) )
the_products = apply(M,1,prod) # compute the product of each set of ages 
M2 = cbind( M, the_products, the_products-16, the_products+16 )
colnames(M2) = c("A1", "A2", "A3", "products", "products-16", "products+16" )
print(M2)



print("The Price of Candy:");
Bs = 8:10
other = Bs - 3 
C_term  = Bs^2 + other^2 - 7*Bs - 7*other 
print(C_term)
descrim = 7^2 - 4 * C_term
print( descrim ) 
M = rbind( Bs, other, C_term, descrim ) 
print(M)
print( c( (7 - sqrt(57) ) / 2, (7 + sqrt(57) ) / 2 ) )
print( c( (7 - sqrt(1) ) / 2, (7 + sqrt(1) ) / 2 ) )
print( 8^2 + ( (7 + sqrt(57) ) / 2 )^2 + 5^2 )



print("Drawing Stones:")

# Try various values for B+W one at a time:
# 
print("B+W=7")
Bs = 3:7
print( rbind( Bs, ( Bs - 2 ) / 5 - (9/10) * ( Bs / 7 ) ) )

print("B+W=8")
Bs = 3:8
print( rbind( Bs, ( Bs - 2 ) / 6 - (9/10) * ( Bs / 8 ) ) )

print("B+W=12")
Bs = 3:12
print( rbind( Bs, ( Bs - 2 ) / 10 - (9/10) * ( Bs / 12 ) ) )

print("B+W=13")
Bs = 3:13
print( rbind( Bs, ( Bs - 2 ) / 11 - (9/10) * ( Bs / 13 ) ) )