# The Tyranny of the Rocket Equation

2019-12-01

# Day 01: The Tyranny of the Rocket Equation

**Description:**

--- Day 1: The Tyranny of the Rocket Equation ---

Santa has become stranded at the edge of the Solar System while delivering presents to other planets! To accurately calculate his position in space, safely align his warp drive, and return to Earth in time to save Christmas, he needs you to bring him measurements from fifty stars.

Collect stars by solving puzzles. Two puzzles will be made available on each day in the Advent calendar; the second puzzle is unlocked when you complete the first. Each puzzle grants one star. Good luck!

The Elves quickly load you into a spacecraft and prepare to launch.

At the first Go / No Go poll, every Elf is Go until the Fuel Counter-Upper. They haven't determined the amount of fuel required yet.

Fuel required to launch a given module is based on its mass. Specifically, to find the fuel required for a module, take its mass, divide by three, round down, and subtract 2.

For example:

For a mass of 12, divide by 3 and round down to get 4, then subtract 2 to get 2.

For a mass of 14, dividing by 3 and rounding down still yields 4, so the fuel required is also 2.

For a mass of 1969, the fuel required is 654.

For a mass of 100756, the fuel required is 33583.

The Fuel Counter-Upper needs to know the total fuel requirement. To find it, individually calculate the fuel needed for the mass of each module (your puzzle input), then add together all the fuel values.

What is the sum of the fuel requirements for all of the modules on your spacecraft?

--- Part Two ---

During the second Go / No Go poll, the Elf in charge of the Rocket Equation Double-Checker stops the launch sequence. Apparently, you forgot to include additional fuel for the fuel you just added.

Fuel itself requires fuel just like a module - take its mass, divide by three, round down, and subtract 2. However, that fuel also requires fuel, and that fuel requires fuel, and so on. Any mass that would require negative fuel should instead be treated as if it requires zero fuel; the remaining mass, if any, is instead handled by wishing really hard, which has no mass and is outside the scope of this calculation.

So, for each module mass, calculate its fuel and add it to the total. Then, treat the fuel amount you just calculated as the input mass and repeat the process, continuing until a fuel requirement is zero or negative. For example:

A module of mass 14 requires 2 fuel. This fuel requires no further fuel (2 divided by 3 and rounded down is 0, which would call for a negative fuel), so the total fuel required is still just 2.

At first, a module of mass 1969 requires 654 fuel. Then, this fuel requires 216 more fuel (654 / 3 - 2). 216 then requires 70 more fuel, which requires 21 fuel, which requires 5 fuel, which requires no further fuel. So, the total fuel required for a module of mass 1969 is 654 + 216 + 70 + 21 + 5 = 966.

The fuel required by a module of mass 100756 and its fuel is: 33583 + 11192 + 3728 + 1240 + 411 + 135 + 43 + 12 + 2 = 50346.

What is the sum of the fuel requirements for all of the modules on your spacecraft when also taking into account the mass of the added fuel? (Calculate the fuel requirements for each module separately, then add them all up at the end.)

Santa has become stranded at the edge of the Solar System while delivering presents to other planets! To accurately calculate his position in space, safely align his warp drive, and return to Earth in time to save Christmas, he needs you to bring him measurements from fifty stars.

Collect stars by solving puzzles. Two puzzles will be made available on each day in the Advent calendar; the second puzzle is unlocked when you complete the first. Each puzzle grants one star. Good luck!

The Elves quickly load you into a spacecraft and prepare to launch.

At the first Go / No Go poll, every Elf is Go until the Fuel Counter-Upper. They haven't determined the amount of fuel required yet.

Fuel required to launch a given module is based on its mass. Specifically, to find the fuel required for a module, take its mass, divide by three, round down, and subtract 2.

For example:

For a mass of 12, divide by 3 and round down to get 4, then subtract 2 to get 2.

For a mass of 14, dividing by 3 and rounding down still yields 4, so the fuel required is also 2.

For a mass of 1969, the fuel required is 654.

For a mass of 100756, the fuel required is 33583.

The Fuel Counter-Upper needs to know the total fuel requirement. To find it, individually calculate the fuel needed for the mass of each module (your puzzle input), then add together all the fuel values.

What is the sum of the fuel requirements for all of the modules on your spacecraft?

--- Part Two ---

During the second Go / No Go poll, the Elf in charge of the Rocket Equation Double-Checker stops the launch sequence. Apparently, you forgot to include additional fuel for the fuel you just added.

Fuel itself requires fuel just like a module - take its mass, divide by three, round down, and subtract 2. However, that fuel also requires fuel, and that fuel requires fuel, and so on. Any mass that would require negative fuel should instead be treated as if it requires zero fuel; the remaining mass, if any, is instead handled by wishing really hard, which has no mass and is outside the scope of this calculation.

So, for each module mass, calculate its fuel and add it to the total. Then, treat the fuel amount you just calculated as the input mass and repeat the process, continuing until a fuel requirement is zero or negative. For example:

A module of mass 14 requires 2 fuel. This fuel requires no further fuel (2 divided by 3 and rounded down is 0, which would call for a negative fuel), so the total fuel required is still just 2.

At first, a module of mass 1969 requires 654 fuel. Then, this fuel requires 216 more fuel (654 / 3 - 2). 216 then requires 70 more fuel, which requires 21 fuel, which requires 5 fuel, which requires no further fuel. So, the total fuel required for a module of mass 1969 is 654 + 216 + 70 + 21 + 5 = 966.

The fuel required by a module of mass 100756 and its fuel is: 33583 + 11192 + 3728 + 1240 + 411 + 135 + 43 + 12 + 2 = 50346.

What is the sum of the fuel requirements for all of the modules on your spacecraft when also taking into account the mass of the added fuel? (Calculate the fuel requirements for each module separately, then add them all up at the end.)

**Input:**

63455

147371

83071

57460

74392

145303

130181

53102

120073

93111

144471

105327

116466

67222

122845

146097

92014

114428

96796

131140

101481

87953

101415

75739

64263

94257

140426

62387

84464

104547

103581

89121

123301

64993

143555

55246

120986

67596

146173

149707

60285

83517

73782

103464

140506

78400

140672

141638

84470

116879

100701

63976

135748

65021

120086

147249

55441

135315

147426

93676

91384

110918

123368

102430

144807

82761

134357

62990

85171

134886

69166

119744

80648

96752

89379

136178

95175

124306

51990

57564

111347

79317

95357

85765

137827

105014

110742

105014

149330

78437

107908

139044

143304

90614

52119

147113

119815

125634

104335

138295

147371

83071

57460

74392

145303

130181

53102

120073

93111

144471

105327

116466

67222

122845

146097

92014

114428

96796

131140

101481

87953

101415

75739

64263

94257

140426

62387

84464

104547

103581

89121

123301

64993

143555

55246

120986

67596

146173

149707

60285

83517

73782

103464

140506

78400

140672

141638

84470

116879

100701

63976

135748

65021

120086

147249

55441

135315

147426

93676

91384

110918

123368

102430

144807

82761

134357

62990

85171

134886

69166

119744

80648

96752

89379

136178

95175

124306

51990

57564

111347

79317

95357

85765

137827

105014

110742

105014

149330

78437

107908

139044

143304

90614

52119

147113

119815

125634

104335

138295

**Part 1:**

```
namespace AdventOfCode2019_01_1
{
const DAY = 1;
const PROBLEM = 1;
export async function run()
{
let input = await AdventOfCode.getInput(DAY);
if (input == null) return;
const fuel = input
.split(new RegExp('\r?\n'))
.filter(p => p.trim().length > 0)
.map(p => parseInt(p))
.map(p => Math.floor(p/3) - 2)
.reduce((a,b) => a+b);
AdventOfCode.output(DAY, PROBLEM, fuel.toString());
}
}
```

**Result:**3464458

**Part 2:**

```
namespace AdventOfCode2019_01_2
{
const DAY = 1;
const PROBLEM = 2;
export async function run()
{
let input = await AdventOfCode.getInput(DAY);
if (input == null) return;
const fuel = input
.split(new RegExp('\r?\n'))
.filter(p => p.trim().length > 0)
.map(p => parseInt(p))
.map(mass =>
{
let fuel = Math.floor(mass / 3) - 2;
let lastfuel = fuel;
for (; ; )
{
let newfuel = Math.floor(lastfuel / 3) - 2;
if (newfuel <= 0) break;
fuel += newfuel;
lastfuel = newfuel;
}
return fuel;
})
.reduce((a,b) => a+b);
AdventOfCode.output(DAY, PROBLEM, fuel.toString());
}
}
```

**Result:**5193796