Anonymous at Wed, 27 Mar 2024 07:13:30 UTC No. 16098934

1) this is essentially saying consider all permutations of 6 symbols (words) that represent numbers, you don't know the value of the digit symbols, but you do know an example of two consecutive words.

NECTAR < TRANCE

notice how the orbits are (N, T), (R, E), (C, A)
let's try to minimize the difference between these numbers by judicious guessing
N and T are the most significant digits, so should only differ by 1. also, N is smaller than T.

E should be as great as possible while R should be as small as possible to minimize the difference between the numbers. so E = 5 and R = 0.

same thing with C and A, but since they are less significant, we use the next best choices C = 4 and A = 1.

this leaves N = 2 and T = 3, which fits the requirements for the most significant digits.

thus, 254310 < 301245 are the consecutive words

the biggest word is 543210, which is ECTNAR.

Anonymous at Wed, 27 Mar 2024 19:49:58 UTC No. 16099783

No

Anonymous at Wed, 27 Mar 2024 21:34:09 UTC No. 16100027

>>16098934
I think dictionary order is the factor here.
NECTAR is the last word in N where T words follow after N: T > N
E > C, T, A, R otherwise next word is NXYYYY
Likewise C > T, A, R otherwise next word NEXYYY
and A > R
Next, the letters are organized least to greatest in trance besides T.
We end with the same conclusion of ECTNAR

Anonymous at Wed, 27 Mar 2024 21:44:55 UTC No. 16100042

This is clearly impossible right? The 1/x must have the one digit number, otherwise you would have one digit number and something else being equal to something smaller than that. But the smallest that 1/x can be then is 1/9 and even if you make 1/y and 1/z as large as possible, being 1/10 and 1/100 you still can not get to that minimum of 1/x.

Anonymous at Wed, 27 Mar 2024 21:45:30 UTC No. 16100045

>>16100042
Negatives exist

Anonymous at Wed, 27 Mar 2024 21:59:28 UTC No. 16100069

>>16100042
Edit: doesn't seem to work with negatives either. I think the best you could do is to have the one digiter in the middle, then subtract the two digiter from that in the hopes of getting a three digiter. But you can not get small enough.

Anonymous at Wed, 27 Mar 2024 22:02:31 UTC No. 16100073

The last word in the dictionary would be CRETAN. Since the word TRANCE immediately follows NECTAR, the alphabetic order is N, E, C, T, A, R. Therefore, the last word with 6 different letters in this order is CRETAN.
Yes, it is possible to solve the equation 1/x = 1/y + 1/z with x, y, z integers and one having one digit, one having two digits, and one having three digits. One solution is x = 30, y = -10, z = 6.
The largest number of dots Rekha can color red is 5,050. She can color the dots on every other row and every other column red, ensuring there is always a blue dot between any two red dots.
Yes, there is always a way to position and orient the checkerboard swatter to kill at least 5 of the 6 flies. The key is to orient the swatter so that at least one fly is on a black square and at most one fly is on a white square.
No, it is not possible for Tian's and Olga's lists of nine products to be identical. This is because the rows and columns contain different sets of numbers, so their products must be different.

Anonymous at Wed, 27 Mar 2024 22:16:47 UTC No. 16100089

>>16100073
>Yes, it is possible to solve the equation 1/x = 1/y + 1/z with x, y, z integers and one having one digit, one having two digits, and one having three digits. One solution is x = 30, y = -10, z = 6.

Where's the one having three digits?