Puzzle of the Week #136 - Packing 31 Shapes in the Space of 25

This would work well as a physical puzzle, if someone wants to have a go at making it.

You have a number of identical objects whose edges are two equal circular arcs. Since each of the shaped is 12cm long and 4cm wide, 25 of them completely fill a 12 x 100 tray as shown.

However it is possible to rearrange them and fit in extra shapes. The very surprising fact is that you can fit SIX extra shapes in. Obviously none of the shapes can overlap each other, or the edges of the box. And you cannot cut the shapes up into smaller pieces.

How is this possible!?

Puzzle of the Week #135 - Odd One Out

Which of these is the odd one out and why?

Puzzle of the Week #134 - Feeling the Chill

‘42 is twice 21, therefore 42 degrees Fahrenheit is twice as cold as 21 degrees Celsius.’

Clearly the logic here is deeply flawed, however there is a sense in which the SPECIFIC conclusion is approximately true, what is it?

Puzzle of the Week #133 - Power Play

123 raised to the power of 987654321 is a number of over 2 billion digits. Please write it out in full.

Only joking! Just give me the final three digits.

Puzzle of the Week #132 - Rows and Columns

Rearrange the rows and columns to find out what this short passage reads:

Puzzle of the Week #131 - Euro Counting

If you wrote the numbers 1 to 20 in English, French and German, which letters of the alphabet would not be used at all?

Puzzle of the Week #130 - Triples

Arrange these 15 ‘triples’ into 5 related words of 9 letters each:

BUR, CAM, CES, EMB, EMM, ENT, ERT, GER, HAL, LEI, LIM, ORT, ROQ, TER, UEF.

Puzzle of the Week #129 - Power Base

What is 5 to the power of 55, minus 5, expressed in base 5?

Puzzle of the Week #128 - Five Cuboids in a Sphere

Fit five cuboids into a sphere of radius 1.

What is the greatest combined volume you can achieve?

Similarly to the Three Rectangles in a Circle puzzle a couple of weeks ago, you’ll find that a great deal of symmetry will help to maximize the volume. Again of course, the answer is not an integer, so I'll be happy to accept an answer to one decimal place.

Good luck!

Puzzle of the Week #127 - Odd One Out

Which of these words is the odd one out?

APPLY  GRANGE  PARROT  PEAK  PLUG  REACH

Notoriously, with odd-one-out questions, you will probably be able to find a reason why each of the words in turn should be the odd one. However, the true solution will be both convincing and satisfying, with even my choice of the odd word serving to support your hypothesis. Good luck!

Free Gift! More Binary Determination Puzzles

Here’s a little gift for you: an excel version of my Binary Determination puzzle.

Just stick it on your desktop and have a play if you ever get bored, or play it first thing in the morning to wake your brain up.

It will randomly generate one of a possible 100 billion billion billion puzzles (which is a lot more than the age of the universe in seconds). When you have completed a row or column the target number will turn green.

I’ve included macros to clear the board (but leave the target numbers as they are), or to begin a completely new game. You will need to enable macros and iterative calculation (circular references). I’ve protected the worksheet to prevent you from inadvertently changing cells that don’t need to be changed, but it’s not password protected so if you want to take a peek under the hood you are perfectly welcome!

You can download the .xlsm file from my Dropbox by following this link:

https://www.dropbox.com/s/qm9uzju27mritcx/binary%20determination.xlsm?dl=0

Enjoy!

Puzzle of the Week #126 - Three Rectangles in a Circle

Fit three rectangles into a circle of radius 1.

What is the greatest combined area you can achieve?

(I usually like to have the solution be a whole number, but this is not possible in this case. It is however possible to express the solution in the form of √a + b, where a and b are whole numbers, but I’m also happy to accept an approximate answer to a couple of decimal places).

Puzzle of the Week #125 - Right Time

I happen to look at the clock and notice that the angle between the hour hand and the minute hand is precisely 90 degrees.

How long, to the nearest second, until the angle between the hands is again 90 degrees?

Bonus Puzzle of the Week #124a - Binary Determination

I’ve introduced a couple of refinements to my Binary Determination puzzle: firstly roughly equal amounts of ones and zeros (previously there were more ones at a ratio of about 2:1); secondly a more concise way of giving the solution

Place a 0 or 1 in each of the empty cells so that in each row and column a pair of 5-digit binary numbers can be read (therefore with decimal values between 0 and 31), such that the product of the two numbers in a particular row or column is shown at the end of that row or column.

Here is an example (using only 3-digit binary numbers), so for instance in the first column, 010 (2) multiplied by 011 (3) is equal to 6, (as there is a 6 at the foot of the first column) and similarly for all of the other columns and rows. Finally, read off the diagonal of each quarter of the grid and convert back into decimal to give the solution (3,3,2,3):

Here is the puzzle:

Puzzle of the Week #124 - Binary Determination

Here’s a brand new type of puzzle that I’ve just invented this week.

Place a 0 or 1 in each of the empty cells so that in each row and column a pair of 5-digit binary numbers can be read (therefore with decimal values between 0 and 31), such that the product of the two numbers in a particular row or column is shown at the end of that row or column.

Here is an example (using only 3-digit binary numbers), so for instance in the first column, 010 (2) multiplied by 011 (3) is equal to 6 (as that is the number at the foot of the first column), and similarly for all of the other columns and rows.

Here is the puzzle:

Puzzle of the Week #123 - Forensic Probability

Imagine two games:

In one a person rolls a dice repeatedly and notes down the result. If a particular number appears three times, any subsequent roll of that number will be ignored. This is continued until ten numbers have been written down.

In another there is a pack of 18 cards, three each with the numbers 1 to 6 on them. 10 cards are drawn at random. The ten numbers are written down.

In both cases the result will be ten numbers between 1 and 6, with no number appearing more than three times. It will be impossible to know whether the ten numbers came from the dice or the cards.

Is it possible to detect, given the results of many repeated trials, which game someone is playing, or are the two games essentially identical? (I’m not for numbers, just general trends that one might look out for).

Paddocks is now out as a pdf ebook.

I know, I know, the printing and postage costs of print-on-demand are not inconsiderable, and whilst I believe Paddocks is better appreciated in its pocket size printed book form, I have now decided to make it available as an ebook.

Not only is it cheaper than the printed book (even with its 40% discount), but also you don't need to pay postage, and it is delivered immediately.

So what's stopping you accessing more than 100 great puzzles (mostly Paddocks, but some other interesting and novel varieties too)?

http://www.lulu.com/shop/elliott-line/paddocks/ebook/product-23381678.html

Puzzle of the Week #122 - Enigmatist

How many different ways are there of arranging the letters of ENIGMATIST, such that no two vowels are adjacent, and no two identical letters are adjacent?

Puzzle of the Week #121 - parkrun PBs

Every Saturday I join around 200,000 other runners and take part in a free 5k run at one of 1000 parks around the world (see http://www.parkrun.com). It's easy to keep statistics on how my times are improving. Alongside here is a table of my twenty fastest parkrun times.

I recorded those times at 16 different parks, and revisited some of them. As well as recording the rank of each parkrun time overall, I also record what its rank was when I ran that time, so for instance when I ran at Long Eaton, it was the second fastest I had run, but because some subsequent runs have been faster, it is now only my 8th fastest time.

Using the information in the table, can you work out in what order I ran the twenty parkruns?

Puzzle of the Week #120 - Quality Control

A company orders in a variety of pieces of metal of lengths:

7cm        17cm     18cm     19cm     25cm     37cm     44cm

46cm     63cm     65cm     82cm     83cm     90cm     100cm

The quality controller, whose task it is to check the length of the incoming parts is correct, has figured out that he can use a straight rod of a particular length, and mark a series of points on it so that all of the lengths in the above list can be measured, either between two of the marks, or from an end to one of the marks. He uses the minimum possible number of marks.

How long is the rod, how many marks were made, and where were they positioned?