Sequence of domino tiles - next term's difference of pips

Question

The problem is as follows:

A set of domino tiles is placed with one next to another as indicated in the diagram below. If the upper half of the next piece is labeled x and the lower half is labeled as y, then find x-y.

The choices given in my book are follows:

1. 2
2. -3
3. 5
4. -5

I found this riddle in my Reason and Logic book from the 2000s. From the style I believe it is adapted from a reprinted version of Martin Gardner's 50's book on Recreational Puzzles

I remember similar puzzles which asked for the least amount of domino pieces which need to be flipped vertically to make the count of pips on the upper and lower halves equal. My method of solving was to sum all the dots, divide this number by two, and see which tiles can be rotated in order to achieve equality.

But in this case I need to find some sort of logic to the ordering of the tiles (or at least I think so), and they appear to be in a random order, which confuses me.

I believe that this question (although it doesn't explicitly say) intends to imply that the set is a double-six. Hence it will have 28 tiles and 126 pieces.

So far I noticed that the third tile starting from the left is swapped upside down in the fourth place, right next to the double zero tile. This could mean that this domino comes from either the set of 3 or the set of 4. But again I couldn't spot anything other than that.

Can someone explain what kind of logic should be used to find the next term in this sequence? Is it just trial and error? I tried finding the difference between the pips in the upper and lower halves, but this didn't help much. Can someone please guide me to a solution? What strategy should be used?

Answer 1

I think the answer is...

Option 4 (-5)

Why?

We can see that the double zero domino flips the domino before it upside-down. Therefore, the next domino must be the 2nd domino(the domino before the double zero domino) flipped upside-down. Hence, x=1 and y=6, and so x - y = 1 - 6 = -5.

Answer 2

Without any further context, the question is on par with number sequence "guessing game", and you won't find any logical path or strategy that leads to the solution. I'm specifically pointing this out because the OP asked for logic and strategy.

But, to my intuition the intended answer looks like

-5 (option 4), with x=1,y=6

which is the same answer as mccraft's, but for a different reason:

Look at the dominoes at the odd positions. From left to right, the top number is decreasing (5 - 4 - 3) while the bottom is increasing (2 - 3 - 4). Now look at the dominoes at the even positions. We can see the bottom as decreasing (1 - 0). For the top, the 6 is supposed to increase, but there's no 7 pips, so it is natural to assume it wraps back to 0 instead. Therefore, I think the top increases to 1, and the bottom "decreases" (wrapping) to 6.

Answer 3

I think that these are the more correct answers:

0, $x=0, y=0$ or 9, $x=8,y=-1$

Because:

On the top row of the dominoes, the value is added and subtracted with consecutive numbers, which means after an addition, there is subtraction, and addition comes first. However, the displayed value cannot be greater than 6 or smaller than 0^. For numbers greater than 6 or smaller than 0, the displayed number is represented with 0^. The first displayed number is its actual value which is 5, also for the second which is 6, and $5+1=6$. The third displayed number is its actual value which is 4, and $6-2=4$. The forth displayed number is 0, but the actual value is 7, because $4+3=7$. The fifth displayed number is its actual value which is 3, and $7-4=3$. For the next number(which is $x$), the actual value is $3+5=8$. However, the displayed value cannot be greater than 6, so $x=0$. For the bottom row, the rules are the same, just that subtraction comes first. Using the rules, we know that the actual value of $y=-1$, however because of the rules, the displayed value of $y=0$. Therefore, by subtracting the two displayed values, the answer is 0. However, the question did not mention that $x$ and $y$ are in their displayed values or their actual values. We can also see that in the question, there are cases in which the question subtracted or added a number's actual value(like as in previously mentioned, $7-4=3$). So, if we subtract the actual values of $x$ and $y$, we get 9.

Notes(please read):

^: For the displayed value cannot be smaller than 0, it is purely my assumption because I could not think of a way to fit negative numbers into dominoes.