Brain Teasers are Back!

Frustrating ? I know !

But it is a Brain Teaser after all :sunglasses:

As ken c would say “enjoy”

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Depending on whether I counted Charlie’s remaining steps correctly, it may be 31 steps.

Well, based on the drawing, Charlie has 14 risers to go. He takes them 5 at a time, except for the last group which is only four strong.

To summarize so far, Albert will finish off with only one riser, Bertie with 3 risers and Charlie with four risers.

You are looking for a number such that when divided by 3, 4 and 5 respectively has 1, 3 and 4 as remainders.

In fact, you are looking for the smallest such number.

19 (I somehow got to 16 steps left for Charlie).

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Well done Eoink.

It helps when tackling these brain teasers if you can count !!! :sunglasses:

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Nicely done Seakayaker

It wasn’t fair Don, it went over 10, so I ran out of fingers.

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You’ll have to take your socks off next time …

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A bit of of tidying up before we move on…

…In essence, Diane simply multiplied by 49 instead of 409.
In other words, whatever the muliplicand was, the product was short-changed by a factor of 409 - 49 = 360.
So the multipkicand x 360 = £328,320
Hence the multiplicand was £912

As before, each circle contains a number which is the sum of the two circles beneath.

Simply fill in the missing numbers !

Top
…-…-…-…-.542
…-…-…-.288 - 254
…-…-203 - 085 - 169
…159 - 044 - 041 - 128
118 - 041 - 003 - 038 - 90

Neat and nicely laid out Seakayaker.
And of course, correct !

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Two discs 3m and 4m

Two discs of radii 3m and 4m are laid on a floor with their centres 5m apart. What is the perimeter of the “figure-eight” shape so formed ?

OK, I know this is more like a flash-back to school maths, but it might get those old gray cells working in one or two forum minds !

Any initial thoughts ?

Radii of 3m and 4m set 5m apart should suggest a bit of pythag.

And circles can be seen as either 360 degrees or better still, 2pi radians (remember them ?)

I’ll post the rest of the calculation tomorrow.

Unless someone beats me to it :sunglasses:

PS, no real need to use radians, degrees work just as well.

Solution

The perimeter (outlined in black), is made up of
An arc subtending (2π - 2α) Radians (in the circle of radius 3m) and
An arc subtending (2π - 2β) Radians (in the circle of radius 4m)

Hence, using an arc length = rθ, we have

Perimeter = 3(6.284 – 1.854) + 4(6.284 – 1.288) m
= 33.3 m

I thought another “Domino” puzzle might help a few insomniacs !

The diagram below shows a standard set of 28 dominoes. They have been set out in a neat pattern.

I have drawn in the outline of one domino, ie 5 - 2.

All you have to do is draw in the outlines of the other 27 !

I found this one very satisfying and logical.

I created a tick list of dominoes to help me keep track of those identified and those outstanding.

Hi Don,
I think this is right, hopefully it’s readable as well:

Both right and readable Mulberry. Well done.

I hope you found it relaxing ?

Same for anyone else giving it a go, now that you can check the answer !

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