Teaser 3029

by Victor Bryant

Published Sunday October 11 2020

Square Jigsaws

I chose a whole number and asked my grandson to cut out all possible rectangles with sides a whole number of centimetres whose area, in square centimetres, did not exceed my number. (So, for example, had my number been 6 he would have cut out rectangles of sizes 1×1, 1×2, 1×3, 1×4, 1×5, 1×6, 2×2 and 2×3.) The total area of all the pieces was a three-figure number of square centimetres.

He then used all the pieces to make, in jigsaw fashion, a set of squares. There were more than two squares and at least two pieces in each square.

What number did I originally choose?

Teaser 3028

by Stephen Hogg

Published Sunday October 04 2020

Rainbow Numeration

Dai had seven standard dice, one in each colour of the rainbow (ROYGBIV). Throwing them simultaneously, flukily, each possible score (1 to 6) showed uppermost. Lining up the dice three ways, Dai made three different seven-digit numbers: the smallest possible, the largest possible, and the “rainbow” (ROYGBIV) value. He noticed that, comparing any two numbers, only the central digit was the same and each number had just one prime factor under 10 (different for each number).

Hiding the dice from his sister Di’s view, he told her what he’d done and noticed, but wanted her to guess the “rainbow” number digits in ROYGBIV order. Luckily guessing the red and orange dice scores correctly, she then calculated the others unambiguously.

What score was on the indigo die?

Teaser 3027

by Andrew Skidmore

Published Sunday September 27 2020

Long Shot

Callum and Liam play a simple dice game together using standard dice (numbered 1 to 6). A first round merely determines how many dice (up to a maximum of three) each player can use in the second round. The winner is the player with the highest total on their dice in the second round.

In a recent game Callum was able to throw more dice than Liam in the second round but his total still gave Liam a chance to win. If Liam had been able to throw a different number of dice (no more than three), his chance of winning would be a whole number of times greater.

What was Callum’s score in the final round?

Teaser 3026

by Graham Smithers

Published Sunday September 20 2020

Party Time

A four-digit number with different positive digits and with the number represented by its last two digits a multiple of the number represented by its first two digits, is called a PAR.

A pair of PARs is a PARTY if no digit is repeated and each PAR is a multiple of the missing positive digit.

I wrote down a PAR and challenged Sam to use it to make a PARTY. He was successful.

I then challenged Beth to use my PAR and the digits in Sam’s PAR to make a different PARTY. She too was successful.

What was my PAR?

Teaser 3025

by Howard Williams

Published Sunday September 13 2020

Please Mind the Gap

Ann, Beth and Chad start running clockwise around a 400m running track. They run at a constant speed, starting at the same time and from the same point; ignore any extra distance run during overtaking. Ann is the slowest, running at a whole number speed below 10 m/s, with Beth running exactly 42% faster than Ann, and Chad running the fastest at an exact percentage faster than Ann (but less than twice her speed).

After 4625 seconds, one runner is 85m clockwise around the track from another runner, who is in turn 85m clockwise around the track from the third runner. They decide to continue running until gaps of 90m separate them, irrespective of which order they are then in.

For how long in total do they run (in seconds)?

Adding Links to Items in Comments

Following on from my previous post about publishing items such as PDF files, images, .. on this site, there is a way in which site users can make such information available which I am now going to describe.

The first step is to upload the material in question to a site somewhere on the internet. This can be any site that allows material to be uploaded for public access. Google Drive is one such site that is available to everyone who has a google account. After an upload has been made it is then necessary to obtain the web address of the material that has been uploaded, its Uniform Resource Locator or URL for short.

To add a link to an upload into a comment it has to be added in a particular form. For example the URL https://brg.a2hosted.com/?page_id=7101 can be made into a link by inserting the following text into a comment:

<a href=”https://brg.a2hosted.com/?page_id=7101″>link</a >

Note that the URL must be in double quotes and the text ‘link’ can be any text that you want to show as the link. Please take care to enter the text exactly as illustrated since any mistake will almost certainly render an unusable link.

Posting Solutions

I have been giving some thought to providing a feature that we used to have on our old site but one we do not currently have here – posting files giving our solutions. This can be done but there will be some limitations that I want to discuss with regular users before I implement anything.

I can authorize others to post here but to do so they would have to be familiar with how to build and edit pages in WordPress and I doubt that this would be feasible for most users of this site (it would also involve care to avoid inadvertently disrupting the operation of other site features). So it seems unlikely that this approach will meet most users needs.

The alternative is that material that users want posted is sent to me so that I can post it on their behalf in an appropriate place. I already have a ‘Solutions’ item under the ‘Current Teaser’ menu item so an obvious way to handle solutions that people want to post is to have another sub-item like the current ‘Solutions’ page but one that links instead to their submitted material. So in addition to a page for each teaser, we would have an associated page giving solutions submitted by users.

The problem with this is that it would add a cost for me in having to build and maintain two pages per teaser and, if many people wanted to submit their solutions, I could end up with significantly more work. And, if people wanted to do what they typically have been doing on the old site – to repeatedly hone their solutions for republication – I could end up withy a lot more editing to keep their published solution as they want it displayed. In practice, however, only a few people have traditionally published material so the load might not prove too heavy.

If we can agree an approach that keeps the workload under control, this approach would allow users to submit material such diagrams and PDF files which this second solutions page would list as clickable links. Also, John Owen (the teaser coordinator for the Sunday Times) has kindly indicated that he might be willing to ask teaser authors if they would allow us to post their ‘official’ solutions. If we adopt this idea, it would need to involve a password mechanism or a publication delay.

The most important way of keeping the workload down would be that anyone who wants to post their solutions (or related material) would have to be careful to ensure it is correct before it is submitted. The second requirement is to submit material in a form that is suitable for publication without the need for further editing or preparation. Fortunately this should not be a problem since WordPress accepts a wide range of formats including PDF files, text files, common image files and even computer programs (see here).

How do people feel about this? Would this be worthwhile and would people accept the need to be more rigorous in proof reading their submissions before submitting them for publication? Are there alternatives that we should consider?

Old Site Archive

Jim Randell has done a fantastic job and has converted all the teaser pages on our old site into PDF files. I have put the files on Google Drive as a public folder here:

https://drive.google.com/drive/folders/1vjtoRVQsdoyYu90bi6lJCTf5TQJVRSq5?usp=sharing

This PDF file that gives more details of the archived teasers and provides clickable links to each archived teaser page (credit to GeoffR for the database that I used to create a part of this file).

The link to the associated attachments is:

https://drive.google.com/drive/folders/1q_cSW3YHYVMeC4VUJJQSHQR5MegSUZ0K?usp=sharing

Do We Need More Headings Here?

Now that we are mostly happy to move to this site, I would like to seek people’s opinions on whether there need to be any more main menu items (note here we have limited space before the menu wraps around).

On the old site, in thinking about preserving the comments on specific teasers, I was struck at how difficult it sometimes is to follow solution ideas on a teaser page because there are a lot of interleaved comments, some of which veer way off topic. For example, people sometimes suggest variations of teasers, or even largely new teasers, which seems fine at the time, but when the comments are read some time later it becomes very difficult to understand which comments relate to the original teaser and which relate to some teaser variation that has been introduced. And sometimes the continuity of interchanges has been broken by exchanges that don’t even involve the teaser at all!

In order to avoid comments here that run into the same problem I would like to request that we keep comments directly related to the teaser in question and that we avoid going off at tangents into related or new teasers (or comments not even related to the teaser being discussed).

But I don’t wish to quash people’s desire to be creative and this means that it may be desirable to allow wider contributions. I am hence thinking of adding a menu item or a page that acts as an anchor for the introduction of teaser variations or more general discussions not related to a specific teaser.

Is this something that we should have? And are there other ‘main menu’ items that people would like to see?

Comments and Threading

I have enabled threaded comments on this site, which means that replies to comments are placed immediately below the comment being replied to. But because of comment indentation there is a limit on the depth of such comments after which no more replies can be threaded in this way.

Another independent choice we have is to place new comments at the top or bottom of the pages on which they appear (i.e. reading top to bottom in chronological order or the reverse).

But there is a relationship between threading and top level comment positioning since if we put new comments at the top, the chronological order of threads is top to bottom while that of new comments is bottom to top.

If we put new comments at the bottom, threaded exchanges that have reached the depth limit can be easily continued by starting a new thread which will appear below the thread in question. Although there may well be other top level threads between the two related threads, often this will not happen and the continued thread will be directly below that it is related to. If, however, we place new threads at the top we are guaranteed to disrupt the continuity of ‘deep’ threads.

Because of this interaction between threading and new comment placement, I prefer to place new threads at the bottom rather than the top when threading is enabled. And I favour threading as I believe it helps a lot in reading and understanding the exchanges that are an essential part of our teaser discussions.

But we can place threads in either position and we can also turn threading off completely so its up to us to decide what we want to do!

So now is the time to let me know what you would prefer!