# Word Arrangement Machine Problem

• Input: All Indians Are My Brothers And Sisters

• Step I: 23 32 12 38 65 17 81

• Step II: 30 70 41 156 328 104 568

• Step III: 568 328 156 104 70 41 30

• Step IV: 20 15 15 9 12 11 10

• Step V: 41 32 33 22 29 28 27

• Step VI: Sisters Brothers My And Indians Are All

As per the rules followed in the steps given above, answer the following question:

New Input: Nothing Is Ever Lost Other Than Change

Question: How many words in step VI for the new input appear in the same position as they appear in the input?

0 because step VI will return: Than Change Lost Other Ever Nothing Is

What is the logic behind the re-arrangement in step VI?

Source: From a local textbook of an institution named 1002105

• Oooh! Great point! But I have noticed it in some places in the textbook and it seems likely that they have themselves picked these from other sources as well, not quite sure though. Jun 30, 2022 at 16:25
• I just found the link to the meta post for proper attribution Jun 30, 2022 at 16:31

Step I:

Substituting $$A = 1, B = 2, ..., Z = 26$$, find the sum of all the consonants and subtract the sum of all the vowels, e.g. $$"All" = (-1) + (12+12) = 23$$.

So the result for the new input would be:

$$39, 10, 30, 36, 26, 41, 26$$

Step II:

For each word in the sentence, multiply the previous result by its position in the sentence (starting with 1) and then add its position if they were numbered in reverse, e.g. "All" is the first word in a 7-word sentence, so we take the previous result ($$23$$), multiply by $$1$$ and add $$7$$ to get $$30$$; for the second word we take $$32$$, multiply by $$2$$ and add $$6$$ to get $$70$$, etc.

So the result for the new input would be:

$$46, 26, 95, 148, 133, 248, 183$$

Step III:

Reorder the results from the prior step in descending order. The results for the new input would now be:

$$248, 183, 148, 133, 95, 46, 26$$

Step IV:

Take the sum of the digits of the previous answer, and add its position in the order (starting from 1), e.g. $$568$$ -> $$(5 + 6 + 8) + 1 = 20$$, $$328$$ -> $$(3 + 2 + 8) + 2 = 15$$, etc.

So the new result is:

$$15, 14, 16, 11, 19, 16, 15$$

Step V:

Double each number and add its position in the sequence, e.g. $$20 * 2 + 1 = 41$$. The new result is:

$$31, 30, 35, 26, 43, 38, 37$$

That's all I have so far, will update once I figure out the rest.

• I had idea till step 5 but not for step 6. Sorry for missing out on this in my question. I'll add it. But it's on same terms as you have said, though I figured that much myself. Jun 30, 2022 at 16:45
• If you already know the answers for all of the steps you don't need to add it to the question, leave that as part of the puzzle. Jun 30, 2022 at 16:46
• Oh, ok. I cancelled the edit. Jun 30, 2022 at 16:47
• The not-so-helpful solution states "Step VI is the original word for the number." Does this helps you at all? Jul 1, 2022 at 11:49
• There are a potentially infinite number of arbitrary transformations we could do to the numbers in the example that would produce the output. I realized now this is the third puzzle you've posted from the same "textbook" that all have ambiguous / nonsensical answers... maybe just stop reading the book. It's not really interesting trying to figure out what the authors were thinking when we've already determined from previous puzzles that they're not following the normal rules of logic. Jul 1, 2022 at 12:59