Submission #7446: The8bitbeast's A2600 Basic Maths in 01:57.13

Basic Maths – Fun with numbers is a game released for the Atari 2600 in 1977. This TAS completes all 8 modes in 7019 frames. Upon completion of each mode, you receive a screen saying 10/10. The TAS shows this screen for a frame each time before moving on to the next mode.

In order to understand the premise of the game, a foundational understanding of the following four arithmetic operations is required.

Let N(S) be the cardinality of a set S, found by counting. To find a+b find two disjoint sets A, B with N(A)=a and N(B)=b then a+b is defined as N(A∪B)

Consider the group of real numbers R with the operation of addition, and two numbers a,b∈R. b will have an additive inverse (–b) which satisfies the equation b+(-b)=0, where 0 is the additive identity. We then define the operation of subtraction by a-b ∶= a+(-b)

Suppose a∈R and b∈Z^+. We define integer multiplication by a×b=∑_(i=1)^b a

Consider the group of real numbers R with the operation of multiplication, and two numbers a,b∈R. b will have a multiplicative inverse (1/b) which satisfies the equation b×(1/b)=1, where 1 is the multiplicative identity. We then define the operation of division by a÷b := a×1/b

Basic Maths (aka Fun with numbers) is a game released for the Atari 2600 in 1977. It features 8 modes, based on definitions 1.0-1.3. Addition – Set Pattern Subtraction – Set Pattern Multiplication – Set Pattern Division – Set Pattern Addition – Random Subtraction – Random Multiplication – Random Division – Random

Suppose the correct answer to a question is the single digit number n, the time taken to enter the answer is 2(5.5-|n-4.5|)

The answer is entered using up or down on the joystick. Up cycles through the numbers 0, 1, 2, 3, … whereas down cycles down through 9, 8, 7, … Once the desired number is reached, the button is used to select it.

Clicking up/down to reach 0 or 9 uses one frame, then clicking B uses another frame. This means that the minimum frames used is 2. Every time the number gets further away from 0 or 9, it will take another 2 frames since the joystick must be released, then pressed again. Continuing this pattern leads to 0 = 2 frames, 1 = 4 frames, 2 = 6 frames and so on. It is worth scrolling up if you have 4 as your answer but down if you have 5 and above. Continuing this pattern gives the below table, and checking each entry shows that it aligns with the formula stated in the theorem.

It is worth getting single digit answers close to either 0 or 9 and manipulating away anything that does not fit this trend. Different questions can be obtained by delaying the answers to the previous questions by a single frame.

Sometimes it is worth tracing back 3-4 questions, to get on a different manipulation seed and therefore better answers.

A good example of this manipulation is the division random pattern (mode 8) as many of the answers are 1 and without manipulation, they can be extremely messy and involve entering remainders.

It is generally ill-advised to have double digit answers unless they are small digits, like 10. If you have a double digit answer, that adds a left press to your answering time, which uses up more time.

The first 4 modes are the set modes. You pick a digit to use for +, -, * or / and that digit is used throughout. For example, in the set multiplication mode, I pick the 1x tables.

The 1x tables set mode will cycle through 1x1 through to 1x9 in a random order, then because it needs a 10th question, it will do one of the 2x tables for the last question. I manipulate it to get 2x4, since 8 is the closest number to scroll to (down through 9, then 8).

Since I would have to answer all of the 1x tables, it makes no difference to manipulate the order they appear in.

This TAS will receive yes votes in the discussion forum.

This is left as an exercise to the reader.

feos: Claiming for judging.

feos: Game cover and cart only say "Basic Math", so shrinking the game name.

Also "all modes" is implied when you don't limit yourself to a specific mode, so clearing the branch.

Great manipulation too, accepting!

despoa: Processing...