expressit

Build instructions

just run it! You may need to run chmod +x first to enable execution.

Goal

Try to make it to the highest round. At each round, you are given a 'target' value, and an 'n' value. You must form a valid expression that creates the target using the given n.

Using the calculator

The calculator is stack-based. n adds the current n to the stack. Other commands take operands from the stack and put back the result. For example, evaluating nn+n/ for n = 3 causes thhe stack to evolve like so: [] -> [3] -> [3,3] -> [6] -> [3, 6] -> [2]. Note the order that /` works in. The stack should always have enough elements for the current operation and only one element in the end. Furthermore, you're limited to 12 commands per round.

commands:

• n -> push n to the stack
• + : add
• - : subtract
• * : multiply
• / : divide
• % : modulus
• f : sum of factors. f 6 = 1 + 2 + 3 + 6 = 12. f 7 = 1 + 7 = 8
• c : collatz function. c (n even) = n/2; c (n odd) = 3*n + 1
• i : iterated collatz function. "xyi" is the collatz funciton applied to x y times.
• t : totient function
• other: do nothing. NOTE: 0,1..9 fall under "other"

a few tips: f and t behave predictably for prime numbers. Plan ahead! The way you solve each target determines the next value of n you get. Try to figure out a few idioms. For example, see if you can figure out an expression that returns 2 no matter what n is. You probably don't need the i function

a few examples:

target = 1
n = 1
n
= 1

Here, we just push n to the stack. Since n = 1, this is all we need. Easy!

target = 1
n = 1
1
stack empty
score: 0

Digits are not a recognized command. Therefore, they are ignored. Since nothing was ever put on the stack, it's empty.

target = 1
n = 1
+
stack empty
score: 0

There should always be enough numbers on the stack for an operation.

target = 3
n = 3
nn
stack overfull
score: 2

At the end, the stack is [3,3]. There should not be more than one number left on the stack.

target = 3
n = 4
nnn/-
= 3

after nnn, the stack is [4,4,4]. After /, it is [1, 4]. After -, it is [3]. note the order for subtraction, which is also used for / and %.

target = 13
n = 3
nn*f
= 13

here, n = 3, so (nn*) = 9. 9f = sum of factors of 9 = 9 + 3 + 1 = 13

target = 16
n = 10
ncc
= 16

we first push 10. c 10 = 10 / 2 = 5. c 5 = 5 * 3 + 1 = 16.

target = 17
n = 5
ntfnn++
= 17

5t = 4, as (1,2,3,4) are all relatively prime with 5. 4f = 4 + 2 + 1 = 7. 7 + 5 + 5 = 17

target = 40
n = 7
nnfi
= 40

n = 7, nf = 8. 8 iterations of the collatz function turns 7 into 40.