Brain Teasers are Back!

Well done Mike. Sleep tight.

There’s more to come !!!

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A Dog’s life !

Many years ago we had a dog. A Border Collie who was very active and enjoyed country walks. She would run back and forth between myself and Mrs D if one of us was trailing behind the other. Mrs D walks at 2 mph, whilst I walk at 4 mph and Becky, the dog, used to run at 10 mph.

One day, I was finishing off a project so Mrs D set off on her walk alone. An hour later I set off in pursuit, taking Becky with me, who immediately hurtled off to catch Mrs D then instantly turned round to return to myself. This too-ing and fro-ing between the two of us continued until I caught up with Mrs D.

How far had Becky run ?

Assume we all travelled at our usual rock-steady speeds. Ignore the length of the dog and assume that no time was lost each time the dog turned around etc……

10 miles?

Well done Eoink.

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Hi Mike,

For someone who was unfamiliar with dominoes, that was some feat.

You might pop down to your local Kiwi toy shop or games shop and pick up a standard box of dominoes. We don’t play too often, but enjoy it when we do.

The grandchildren seem to prefer using them as building blocks !

Something for everyone.

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I’m not sure this one justifies a place in “Brain Teaser”. It’s straightforward.

OK, it needs a bit of concentration and in this day and age, that seems to be lacking in many respects. Here goes …

The numbers in the columns, the rows and the two diagonals add up to their respective totals along the bottom, down the righthand side and in the two boxes, one at the top (70) and one at the bottom (106) of the righthand side.

All you need to do is fill in the missing numbers in the spreadsheet.

If you’ve attempted the “spreadsheet” puzzle above but can’t copy/paste etc, just let us all know by quoting a few empty boxes, eg the two missing numbers in the third row between the “2” and the “15”

What is the numerical value of each symbol: aeroplane; school bus; racing car; digger; and locomotive ? Each one is an integer and the sums of the rows and columns reflect the appropriate values.

Plane = 9
Train = 3
Car = 4
Digger = 7
Bus = 2

All present and correct sir !

Well done Eoink.

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Hi Mike, close, in fact very close, but…

…you might like to check that diagonal line running “bottom left …16” up to “top right 5”.

It needs to total 70.

At the moment it seems to total 65.

Now that Mike has familiarized himself with dominoes, I thought another 28 domino board might be worthwhile.

I found the first half dozen or so quite straightforward to identify then …

… it was a bit more challenging than the previous version !

PS. you should be able to copy and paste or save and paste the diagram into Word or Powerpoint or similar program so as to print it. Much easier to work on.

Also, if you can’t scan or photograph your end product, just quote a couple of domino positions.

For those of you with a standard set of 28 dominoes, here is a neat little party trick (well, Xmas is only 3 months away and a bit of practise won’t go amiss !)

From the face-down set of dominoes, you (the magician) remove one domino, or ask one of your guests to blindly select one of the dominoes for you. There is only one condition, the selected domino must NOT be a double !

Your guests then have the task of laying out the remaining 27 dominoes in a straight line according to the usual rules, ie 6 to 6, 4 to 4 etc. You are not allowed to watch this process nor see the end result.

When the line is complete, without looking, you announce the value of the two exposed ends of the line. You won’t declare which end is which, just the two exposed values.

Of course you know what these two values will be, because they are the values on the 28th domino which is in your hand.

This derives of course, from the fact that a full set of dominoes will form a complete circle if laid end to end according to the usual rules.

At the Muddletown election in November 2019, 5,473 votes will be cast.

The LibDem candidate will be elected by a majority of 18 over the Conservative (an overwhelming victory in this day and age !), by 146 over the Independent, and 575 over the Labour candidate…

How many votes will be cast for each candidate ?

1553, 1535, 1407, 978 (possibly, my mental arithmetic isn’t what it was, I’m reduced to using fingers to hold digits when subtracting).

Looks like you still have five fingers on each hand.

Well done !

A Wheel Fallacy !

This one might well have gone into the “Use of English” thread !! The explanation of what is happening needs to be accurately and concisely described.

Of course there is a bit of maths, both approximations (Pi anybody ?) and precise answers.

In other words, something for everybody. (I wish !)

In the diagram below, the wheel makes one complete revolution and rolls along the line A to B. In doing so it has travelled a distance equal to the circumference of the wheel.

For the mathematically minded, we can calculate this distance approximately, but calculating it exactly isn’t possible in most cases.

For example, let’s take a typical bicycle wheel with a 28” diameter. A common approximate calculation involves multiplying the diameter by 22 and dividing by 7 giving 88” for AB. But this is tad on the high side. A better approximation is obtained by multiplying by 355 and dividing by 113 giving 87.9646…. and an even better approximation is obtained by ……well, give it a go……but exact isn’t on the menu.

Now, if we put a mark on the wheel at the point of contact with the ground at A, this mark would describe an arc as the wheel moved from A to B. At the halfway point, that mark would be at the top of the wheel, 28” above the line AB. The length of this arc can be calculated precisely …………. Well, give it a go. The answer is precise.

Now for the Use of English.

The diagram shows a smaller circle, concentric with the wheel and represents (say) a brake disc which is fixed and rotates with the wheel. It will also make one revolution as the wheel makes one revolution. In doing so, a mark on the brake disc at C will end up at D at the same moment the wheel arrives at B. Clearly the distance CD is identical to AB but that is substantially more than the circumference of the brake disc.

In a few words (ie please be concise) just clearly explain this apparent fallacy !

Thought I had better clear up a few outstanding (in the sense of “not yet completed” !) ones.

I started by filling in the “10” towards to the bottom of the second column, then the “28” in the same row right hand column and so on …

Here are the first few dominoes that I identified. This was simply a “trawl” of unique “pairs” that made a specific domino. So 6-6 was pretty easy to spot as were 4-4 and 3-3. The 2-6 and 0-2 would leave “orphaned” tiles unless paired up as shown. And the 2-6 was unique anyway.

The next step wasn’t quite so easy …