Lia's Failure

Author: mistertfy64

(The maximum score for this problem is 1010000 points.)

Despite Lia's best efforts to remain as an Angel, she failed to remain as an angel. But Lia isn't going out that easily! Lia knows that the angels have a secret codeword they can use to indicate their status. Before getting fired, the upper angel failed to properly contain the information in the codeword, so Lia managed to snag a note that contains the codeword. Also despite Lia's best efforts (again), when she snagged the paper with the codeword, the paper ripped in pieces, and Lia didn't actually get the codeword on the piece of paper.

Not all hope is lost for Lia, since she doesn't want to be viewed as a Failure, Lia gets some clues of the codeword (if you want to know, the codeword is on the top, and the clues are under the codeword, note that this is here for clarification and storytelling purposes and is not considered to be a clue):

• The odd-numbered letters (first, third, fifth, seven, ninth) are all consonants.
• The first two letters of the word contain the first two letters of the alphabet in some order.
• The word is modern. (In this clue, "modern" means the word usage is higher in recent times, rather than a very old time, e.g. the year 1950. The source is for this Google Books' Ngram viewer.)
• Exactly three vowels appear in the word, and the vowels are different.
• There is exactly one n where the n-th letter of the alphabet appears once more than the n-1-th letter of the alphabet. (e.g., Z appears 3 times, Y appears 2 times.)
• There is exactly one occurrence of the letter T in the word.
• There is exactly one k where there is exactly one n where the k+x-th letter of the alphabet appears at position k and the k+x+n-th letter of the alphabet appears at position k+n where x is a constant. (e.g., the word ABSOLUTE is valid if k = 1, n = 1, and x = 0.)
• If the word was rewritten where each letter was in alphabetical order where the first letter is the n-th letter of the alphabet, the last letter is the n+19th letter in the alphabet (e.g., the word DOWN is valid: D is the 4th letter of the alphabet, and W is the (4+19)rd or 23rd letter of the alphabet).
• There are nine distinct letters in the word. Therefore, one of the nine distinct letters will appear twice.
• If each letter in the word was converted to a number in its order in the alphabet (e.g., A = 1, B = 2, C = 3), the sum of the numbers is 105.
• The string AMEN is a subsequence of the word. (i.e., there is a way to remove letters from this word, possibly all or none, without changing the order of the remaining letters where the string AMEN will remain.)
• There are three letters in the word (not necessarily continuous) that come from the first five letters of the alphabet.
• There are six letters in the word (not necessarily continuous) that come from the first half (i.e., first 13 letters) of the alphabet.
• If each letter in the word was converted to a number in its order in the alphabet, there will be four prime numbers.
• The word has a positive connotation. (In this clue, "positive" means "good" or "constructive", e.g., BLESSING is considered "good", and CREATION is considered constructive.)
• If each letter in the word was converted to a number in its order in the alphabet, the product of the numbers is 697132800.
• The word is a synonym of the word "ANGEL". (In this clue, SPIRIT is considered a valid word.)
• The string MENT is a substring of the word. (i.e., the exact string MENT will appear in this word in this order somewhere in the word)
• The letters A, E, H, S, appear in the word exactly once in some order.
• If each letter in the word was converted to its corresponding number in the ASCII table in its binary representation, the total number of 1s will be 18 less than the total number of 0s. (A is 01000001, B is 01000010, C is 01000011, and so on.)

Lia knows the codeword, when spelt correctly, is ten letters long. Lia also remembers that some clues are false (which means to consider the opposite/negation of that clue) if it's written in a particular way. But oh no! Lia failed to remember what that "particular way" is, since the its somewhat a obscure detail and no one actually remembers an obscure detail correctly.

The correct password is the codeword in all capital letters.

Correct Answers