Puzzle 1
x <- 1.1
a <- 2.2
b <- 3.3

x*a*b
## [1] 7.986
y <- x*a
y*b
## [1] 7.986
3*x^3 + 2*x^2 + 1
## [1] 7.413


Puzzle 2
a <- c(1,2,3,4,5,6,7,8)
b <- c(7,6,5,4,3,2,1)
z <- c(a,b)
print(z)
##  [1] 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1
a <- c(1,2,3,4,5)
rep(a,a)
##  [1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
b <- c(5,4,3,2,1)
rep(b,a)
##  [1] 5 4 4 3 3 3 2 2 2 2 1 1 1 1 1


Puzzle 3
a <- runif(2)
print(a)
## [1] 0.7285874 0.3319036
r = sqrt((a[1]^2)+(a[2]^2))
print(r)
## [1] 0.8006245
theta = atan((a[2])/(a[1]))
print(theta)
## [1] 0.4274548


Puzzle 4
queue <- c("sheep", "fox", "owl", "ant")
print(queue)
## [1] "sheep" "fox"   "owl"   "ant"
queueA <- c(queue, "serpent")
print(queueA)
## [1] "sheep"   "fox"     "owl"     "ant"     "serpent"
queueB <- c(queueA[2:5])
print(queueB)
## [1] "fox"     "owl"     "ant"     "serpent"
queueC <- c("donkey", queueB)
print(queueC)
## [1] "donkey"  "fox"     "owl"     "ant"     "serpent"
queueD <- c(queueC[1:4])
print(queueD)
## [1] "donkey" "fox"    "owl"    "ant"
queueE <- c(queueD[c(1,2,4)])
print(queueE)
## [1] "donkey" "fox"    "ant"
queueF <- c(queueE[c(1,2)],"aphid",queueE[3])
print(queueF)
## [1] "donkey" "fox"    "aphid"  "ant"
length(queueF)
## [1] 4
queueF[1]
## [1] "donkey"
queueF[2]
## [1] "fox"
queueF[3]
## [1] "aphid"
queueF[4]
## [1] "ant"


Puzzle 5
a <- 1:100 
b <- which (a %% 2 != 0 & a %% 3 != 0 & a %% 7 != 0)
print(b)
##  [1]  1  5 11 13 17 19 23 25 29 31 37 41 43 47 53 55 59 61 65 67 71 73 79 83 85
## [26] 89 95 97