54*. In the language of the Tru-la-la tribe, a word is any sequence of 10 digits 0 and 1. It is known that two words are synonyms if and only if one can be obtained from the other by a series of operations of the following kind: from the word, several consecutive digits, the sum of which is even, are erased, after which the erased digits are written back in the same place, but in reverse order. How many words of the Tru-la-la language can be written that differ in meaning?
89.54. Answer. 56 words. Instruction. Consider all words of the Tru-lya-ya tribe language of the form $11 \ldots 100 \ldots 0100 \ldots 0$. Prove that any word can be brought to such a form. To prove that these words are distinct, use the following quantity defined for any word in the Tru-lya-ya language: the number of zeros to the right of which there is an odd number of ones. Prove that this quantity does not change when performing the operations described in the problem conditions.