Brain Teasers are Back!

Mike,

In the diagram you posted, the “vertical” 6-2 domino that you outlined can’t represent the 6-2 domino because you have already allocated the “6” to the 6-6 domino above and there is only one 6-6 location in the diagram.

This means that the horizontal 2-6 domino that you have highlighted with a question mark has got to be the 6-2 domino (or the 2-6 domino, they are the same domino). There are no other pairs of 6-2 in the diagram.

Yes, that is why I was asking if they can be reversed. Back to the drawing board.

So is your 6-4 a 4 - 6 then, because I can’t get it to work?

Hi Mike,

Yes, the 6-4 domino can be a 6-4 or a 4-6 depending on its orientation. However, in the diagram, that particular domino has been laid N-S with the six dots at the N end and the four dots at the South end.

The 6-2 domino that you highlighted with ? mark has been laid E-W with the six dots at the E side and the two dots at the W side.

In a standard box of 28 dominoes, there is only one of each denomination starting at 6-6 and working down to 0-0. Each domino is represented in the diagram. Each appears only once.

Each domino is a 2x1 rectangular tile. It is divided into two halves, each a 1x1 square. Each square contains 0 to 6 dots. The tile with the most dots has 6 dots in each square, ie 12 dots in total. You have identified where this tile is placed in the diagram. You have also identified the 6-2 domino (by eliminating one of two possibilities because of the position of the 6-6 domino.) I marked the 6-4 domino in the starter diagram.

Only 25 more to go … :sunglasses:

Here is the list of 28 domino tiles.

You will see that I have ticked off 6-4 (aka 4-6 in my list)

You could now tick off 6-6 and 6-2 (aka 6-6 and 2-6 in my list)

Does this help ?

Yes, I mis-interpreted this…

An easy one just to get the grey matter flowing … :sunglasses:

The number in each circle is the sum of the numbers in the two circles below it.

Complete the numbers, or at least, quote the number at the top of the pyramid.

1393
803,590
455,348,242
248,207,141,101
110,138,69,72,29

I think.

Eoink, you think right !

Well done.

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Same rules, but hopefully just a smidgen more interesting ?

Oh, and the bottom two lines are the important ones this time !

Nicely done Erich.

Looks as if the “pyramids of circles” have overshadowed the “domino cross”

I will post my domino solution tomorrow unless someone else gets there before me or asks for clarification as to the task !

I set up three equations to solve the values in the circles labeled b; e and f in Erich’s solution. ie,

128 + b = e
30 + b = f
e + f = 362

This soon delivered b, quickly followed by e and f

The rest of the pyramid was solved with relatively simple mental arithmetic.

I’ll have a look at it later Don.

A few pictures of dominoes Mike.

I feel as if you are working blindfold if you have never played dominoes before !!

The four in the top line are all the same domino, and would be depicted as 4-3 or 3-4 in the brain teaser.

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It has me stumped I’m afraid. I sense there is a “pattern of elimination” to solve it, but it is eluding me.

You are correct. There is a systematic way of solving the puzzle.

I started by looking for unique pairs of adjacent numbers, eg 6-6. There is only one such pair, ie at the top. This pair therefore must form the 6-6 domino. I drew a rectangle around it and ticked off the 6-6 domino in my standard list.

I then looked for pairs of 5-5. But there was more than one such possible sets. So at this stage I was unable to decide which of those pairs formed the 5-5 domino. And I moved onto the 4-4 search.

I worked my way through all 28 standard dominoes, looking for unique pairs and I think I found about half a dozen. But it was a good start.

I then noticed that a few numbers would be left “orphaned” ie isolated, without an adjoining square unless they were partnered with a specific adjoining square. This meant I could eliminate all other pairs of that combination and be certain that I had found a domino, outlined it as such, ticked it off my list, and moved on.

It took a bit of careful thinking, but it all worked out in a satisfyingly way !

The diagram above highlights the first six dominoes that I found.

The sequence in which I found them was

6-4 (given)
6-6
2-6
1-4
0-2
0-0

This was achieved with just a single pass through the list of standard dominoes starting at 6-6 and working along my list back to 0-0.

In each case, the domino was unique, ie there were no other combinations of those pairs of numbers anywhere else on the board.

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Given that there can’t be any “orphans”, the next 4 dominoes that I found, were pretty easy to spot !

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Thank for the tip @Don, I think I finally got there…