Calculation puzzle 009

Well, we are continuing with what is x series.

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| 3   11   9 |
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v
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| 8   17   5 |
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v
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| 9   17   2 |
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v
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| 6   22   x |
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As the arrows indicate the box below, there must connection with the boxes. Try to find x through applying a method that is valid for all the boxes.

I tried to solve it but to no avail. I added all the numbers in the boxes; 3+11+9=23, 8+17+5=30, 9+17+2=28 and no way to go, no result, no logical numbers here. In the 2nd and 3rd boxes, the center number is 17, and 1st number increases by 1 but the last number decreases by 3, I still couldn't find any possible algorithm there.

Source: The question is asked in YTUYOS 2017 booklet A, question no: 58. These are the questions asked in university entrance exam for international students in Turkey. These types of questions should not take more than 2 minutes to solve and generally they do have only one answer. In case they have more than one then the question is cancelled. The universities sometimes provide the answer to all questions after the exam. The correct answer was given in the booklet, and I added it here in order to help anyone who tries to solve the question.

Possible solution is 5.5 if decimal numbers are allowed consider the sequence 13,9,5,1 it goes down by 4 each time and so if you take the first and last number of the box add it together and multiply it by 2 and then take away the middle number and then do this to the box following is series indicated by the arrows, it will form this sequence

• Decimals are not allowed. However, your answer seems very logical. I have seen a solution by a teacher to these questions, even there he skipped this specific question noting that no one had found a proper solution until that time. Furthermore, he claimed that this question might be wrong itself. Sometimes universities make mistake by making typo or asking the questions even themselves can't solve. Thank you for your solution, @Deepthinker101. Jul 17, 2020 at 9:40
• Yes I felt that way when I figured out this solution. By the way... although some of your questions on here have been food for thought and so I thank you for posting them, I personally don't like you to put the answer here. It makes me tempted to look and doing so would ruin the puzzle! I think that is possibly why your posts don't get a high ranking inspite if the fact some questions are good Jul 17, 2020 at 10:35
• thank you for pointing out. I didn't think that way. From now on I think I will not give out the answers. Also I appreciate that you like my questions here. I would personally grade these types of questions 2 or 3 over 5 in originality and difficulty level. I wish I could add real IQ questions, original puzzles. Editing, making shapes takes time here in this platform. To come over high-quality questions is also very difficult. I think I will try to add them here in the future when I see them. Thanks again. Jul 17, 2020 at 19:54

If we add three number given inside each rectangle and subtract a number to get number in middle we can find a increasing sequence .ie :
$$3$$ + $$11$$ + $$9$$ = $$23$$ - $$12$$ = $$11$$ ( middle number)
$$8$$ + $$17$$ + $$5$$ = $$30$$ - $$13$$ = $$17$$ ( middle number)
$$9$$ + $$17$$ + $$2$$ = $$28$$ - $$11$$ = $$17$$ ( middle number)
$$6$$ + $$22$$ + $$8$$ = $$36$$ - $$14$$ = $$22$$ ( middle number) Here , we can observe a increasing sequence by $$1$$ i.e : $$11$$,$$12$$ ,$$13$$ ,$$14$$ ..

• But the sequence does not follow from top to bottom like the arrows indicate Jul 16, 2020 at 8:54
• Also you can get the sequence by ignoring the middle number entirely just add the first and last one Jul 16, 2020 at 8:57