Step 1
Notice the pattern. Enter in small inputs and see if you can spot what the game is doing to your input and what the grid represents.
Step 2
The first column corresponds to factors of the input. The other columns seem to be doing something slightly different, however...
Step 3
The arrows are pointing between the numbers and not directly at them... Maybe something is being changed about our answer.
Step 4
After inputting something like 9, realize that the arrow just adds a 0 where its pointing when calculating the factors for that column. This is consistent with the first column.
Step 5
So we need a number like abc, such that 0abc, a0bc, ab0c, abc0 are divisible by 1-9. We still don't know how long the answer is, but we can still go forward.
Step 6
Recall the divisibility rules for 1-9.
1,2,3,4,6 are factors if 5,7,8,9 are factors.
Step 7
A number ending in 000 is a multiple of 1000, and is always divisible by 5 and 8.
Step 8
To make 7 and 9 a factor, we need to determine the digits at the front. Divisibility by 9 requires the digits to sum to a multiple of 9. We'd also like the digits at the front to be divisible by 7. Is there an easy expression that is clearly divisible by 7 and 9, regardless of any 0s added in between?
Step 9
Yes! A row of 9 7s as such: 777777777. Their sum is 7*9, and each digit is clearly divisible by 7. Combining the two, an answer is 777777777000. Any zero that is added anywhere will not impact our construction.
Dangit! I'd figured out everything through step 8, but just didn't see that final question in #8. (And I thought I was so close with <rot13>fvkgl-guerr gubhfnaq</rot13>. Thanks for writing this out as a series of hints!
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777600 look this mf damn seven.......
25200
567000 was so close...
im red green colourblind
Fun one!
Solution using only elementary school math:
Step 1
Notice the pattern. Enter in small inputs and see if you can spot what the game is doing to your input and what the grid represents.Step 2
The first column corresponds to factors of the input. The other columns seem to be doing something slightly different, however...Step 3
The arrows are pointing between the numbers and not directly at them... Maybe something is being changed about our answer.Step 4
After inputting something like 9, realize that the arrow just adds a 0 where its pointing when calculating the factors for that column. This is consistent with the first column.Step 5
So we need a number like abc, such that 0abc, a0bc, ab0c, abc0 are divisible by 1-9. We still don't know how long the answer is, but we can still go forward.Step 6
Recall the divisibility rules for 1-9. 1,2,3,4,6 are factors if 5,7,8,9 are factors.Step 7
A number ending in 000 is a multiple of 1000, and is always divisible by 5 and 8.Step 8
To make 7 and 9 a factor, we need to determine the digits at the front. Divisibility by 9 requires the digits to sum to a multiple of 9. We'd also like the digits at the front to be divisible by 7. Is there an easy expression that is clearly divisible by 7 and 9, regardless of any 0s added in between?Step 9
Yes! A row of 9 7s as such: 777777777. Their sum is 7*9, and each digit is clearly divisible by 7. Combining the two, an answer is 777777777000. Any zero that is added anywhere will not impact our construction.Dangit! I'd figured out everything through step 8, but just didn't see that final question in #8. (And I thought I was so close with <rot13>fvkgl-guerr gubhfnaq</rot13>. Thanks for writing this out as a series of hints!
Nice design! And the final answer is much much simpler than I thought. (+_+)
Hint (encoded in base64/UTF-8 to avoid spoiler):
Cool puzzle!