We need your help now
Support from readers like you keeps The Journal open.
You are visiting us because we have something you value. Independent, unbiased news that tells the truth. Advertising revenue goes some way to support our mission, but this year it has not been enough.
If you've seen value in our reporting, please contribute what you can, so we can continue to produce accurate and meaningful journalism. For everyone who needs it.
Sign in. It’s quick, free and it’s up to you.
An account is an optional way to support the work we do. Find out more.
By continuing, you are indicating that you accept our Terms of Service and Privacy Policy.
MATHS WEEK STARTED yesterday and, as is our annual tradition, we’re setting our readers some puzzles. Give them a go!
Day Two - Happy Birthday Quaternions
Of course all the brother’s sums isn’t done in the digs. He does be inside in a house in Merrion Square doin’ sums as well. If anybody calls, says the brother, tell them I’m above in Merrion Square workin at the quateernyuns, says he, and take any message. There does be other lads in the same house doin’ sums with the brother. The brother does be teachin’ them sums. He does be puttin’ them right about the sums and the quateernyuns.
Myles na gCopaleen, Cruiskeen Lawn
16 October is the birthday of quaternions. Quaternions are sets of four numbers that can be used to describe the position and orientation of bodies in space. They are useful for moving objects in computer animation and manoeuvring spacecraft.
They were discovered on this day in 1843, by William Rowan Hamilton while walking along the towpath of the Royal Canal at Broombridge. The occasion and location is marked with a plaque and the birthday is celebrated by the Irish mathematical community with the annual Hamilton walk.
For Myles, quaternions represented advanced mathematics impenetrable to all but the experts at the Dublin Institute for Advanced Studies (in Merrion Square) and of course “the brother”.
You will be relieved that our puzzles today are about birthdays, not quaternions.
1. John and Mary celebrate their birthdays on the same day. Mary is now four times John’s age. In four years she will be twice John’s age. How old is Mary now?
2. When I asked her how old she was, my friend smiled and said cryptically, “The day before yesterday I was twenty-two, but next year I’ll be 25.
When was her birthday, and on what date did the conversation take place?
Come back tomorrow for the answers to today’s puzzle.
The Maths Week puzzles this year are presented by Colm Mulcahy, professor emeritus of Mathematics at Spelman College, USA, and adjunct professor with Calmast at South East Technological University. Colm is chairperson of the Martin Gardner Foundation USA, and the curator of the website mathsireland.ie
Saturday’s puzzle: The answer
A. You actually end up earning 1% less that you did originally. For every €100 you earn at
the outset, after the 10% raise you earn €110, but then after the later 10% reduction
that drops €11 to only €99. That’s a 1% loss overall.
B. Your brother actually ends up earning the same as he did originally. For every €100 he
earns at the outset, after the 25% raise he earns €125, but then after the later 20%
reduction that drops back €25 to the original €100. That’s because 20% of €125 is a fifth
of it, which is €25.
C. Your sister actually end up earning 2% more that she did originally. For every €100 she earns at the outset, after the 20% raise she earns €120, but then after the later 15% reduction that drops €18 to only €102. That’s because 15/100 times €120 is €18.
D. Your friend actually end up earning 5% less that she did originally. This is very surprising. For every €100 she earns at the outset, after the 25% raise she earns €125, but then after the later 24% reduction that drops €30 to only €95. That’s a 5% loss overall. Note that 24/10 times €125 is €30.
E. The overall pay cut is a little over 67%: for every €100 you earn at the outset, you end
up earning about €32.77. Can you explain why, using the kind of reasoning we used
above?
Say you start with €100…
That’s a total loss of €67.33 from the original €100 , so overall, a reduction of about 67%.
Moral: percentages are tricky! They don’t work like ordinary addition and subtraction: what gets added and subtracted to modify amounts repeatedly involves several multiplications. The final results are not easy to predict. As we have just seen, it’s even hard to predict qualitatively: will we come out ahead, even, or behind?
To embed this post, copy the code below on your site
Mary is 8, the friends birthday is 31December and the conversation took place on the 2 Jan.
@Gerard Carthy: typo. 1st was the conversation.
@Gerard Carthy: The conversation took place on the 1st of January.
@John Fagan: Ah right. She was 22 on 30th Dec, 23 (her birthday) on 31st.
Its now 1st of Jan so she’ll be 24 this year and 25 next year.
Didn;t twig it.
@Gerard Carthy: Mary is 4
@OConnelj: Apologies Gerard, you are correct. My bad. :(
Use precise geolocation data. Actively scan device characteristics for identification. Store and/or access information on a device. Personalised advertising and content, advertising and content measurement, audience research and services development.
These cookies are necessary for the website to function and cannot be switched off in our systems. They are usually only set in response to actions made by you which amount to a request for services, such as setting your privacy preferences, logging in or filling in forms. You can set your browser to block or alert you about these cookies, but some parts of the site will not then work.
These cookies are set by a range of social media services that we have added to the site to enable you to share our content with your friends and networks. They are capable of tracking your browser across other sites and building up a profile of your interests. This may impact the content and messages you see on other websites you visit. If you do not allow these cookies you may not be able to use or see these sharing tools.
These cookies may be set through our site by our advertising partners. They may be used by those companies to build a profile of your interests and show you relevant adverts on other sites. They do not store directly personal information, but are based on uniquely identifying your browser and internet device. If you do not allow these cookies, you will experience less targeted advertising.
These cookies enable the website to provide enhanced functionality and personalisation. They may be set by us or by third party providers whose services we have added to our pages. If you do not allow these cookies then these services may not function properly.
These cookies allow us to count visits and traffic sources so we can measure and improve the performance of our site. They help us to know which pages are the most and least popular and see how visitors move around the site. All information these cookies collect is aggregated and therefore anonymous. If you do not allow these cookies we will not be able to monitor our performance.
Cookies, device or similar online identifiers (e.g. login-based identifiers, randomly assigned identifiers, network based identifiers) together with other information (e.g. browser type and information, language, screen size, supported technologies etc.) can be stored or read on your device to recognise it each time it connects to an app or to a website, for one or several of the purposes presented here.
Advertising presented to you on this service can be based on limited data, such as the website or app you are using, your non-precise location, your device type or which content you are (or have been) interacting with (for example, to limit the number of times an ad is presented to you).
Information about your activity on this service (such as forms you submit, content you look at) can be stored and combined with other information about you (for example, information from your previous activity on this service and other websites or apps) or similar users. This is then used to build or improve a profile about you (that might include possible interests and personal aspects). Your profile can be used (also later) to present advertising that appears more relevant based on your possible interests by this and other entities.
Advertising presented to you on this service can be based on your advertising profiles, which can reflect your activity on this service or other websites or apps (like the forms you submit, content you look at), possible interests and personal aspects.
Information about your activity on this service (for instance, forms you submit, non-advertising content you look at) can be stored and combined with other information about you (such as your previous activity on this service or other websites or apps) or similar users. This is then used to build or improve a profile about you (which might for example include possible interests and personal aspects). Your profile can be used (also later) to present content that appears more relevant based on your possible interests, such as by adapting the order in which content is shown to you, so that it is even easier for you to find content that matches your interests.
Content presented to you on this service can be based on your content personalisation profiles, which can reflect your activity on this or other services (for instance, the forms you submit, content you look at), possible interests and personal aspects. This can for example be used to adapt the order in which content is shown to you, so that it is even easier for you to find (non-advertising) content that matches your interests.
Information regarding which advertising is presented to you and how you interact with it can be used to determine how well an advert has worked for you or other users and whether the goals of the advertising were reached. For instance, whether you saw an ad, whether you clicked on it, whether it led you to buy a product or visit a website, etc. This is very helpful to understand the relevance of advertising campaigns.
Information regarding which content is presented to you and how you interact with it can be used to determine whether the (non-advertising) content e.g. reached its intended audience and matched your interests. For instance, whether you read an article, watch a video, listen to a podcast or look at a product description, how long you spent on this service and the web pages you visit etc. This is very helpful to understand the relevance of (non-advertising) content that is shown to you.
Reports can be generated based on the combination of data sets (like user profiles, statistics, market research, analytics data) regarding your interactions and those of other users with advertising or (non-advertising) content to identify common characteristics (for instance, to determine which target audiences are more receptive to an ad campaign or to certain contents).
Information about your activity on this service, such as your interaction with ads or content, can be very helpful to improve products and services and to build new products and services based on user interactions, the type of audience, etc. This specific purpose does not include the development or improvement of user profiles and identifiers.
Content presented to you on this service can be based on limited data, such as the website or app you are using, your non-precise location, your device type, or which content you are (or have been) interacting with (for example, to limit the number of times a video or an article is presented to you).
With your acceptance, your precise location (within a radius of less than 500 metres) may be used in support of the purposes explained in this notice.
With your acceptance, certain characteristics specific to your device might be requested and used to distinguish it from other devices (such as the installed fonts or plugins, the resolution of your screen) in support of the purposes explained in this notice.
Your data can be used to monitor for and prevent unusual and possibly fraudulent activity (for example, regarding advertising, ad clicks by bots), and ensure systems and processes work properly and securely. It can also be used to correct any problems you, the publisher or the advertiser may encounter in the delivery of content and ads and in your interaction with them.
Certain information (like an IP address or device capabilities) is used to ensure the technical compatibility of the content or advertising, and to facilitate the transmission of the content or ad to your device.
Information about your activity on this service may be matched and combined with other information relating to you and originating from various sources (for instance your activity on a separate online service, your use of a loyalty card in-store, or your answers to a survey), in support of the purposes explained in this notice.
In support of the purposes explained in this notice, your device might be considered as likely linked to other devices that belong to you or your household (for instance because you are logged in to the same service on both your phone and your computer, or because you may use the same Internet connection on both devices).
Your device might be distinguished from other devices based on information it automatically sends when accessing the Internet (for instance, the IP address of your Internet connection or the type of browser you are using) in support of the purposes exposed in this notice.
The choices you make regarding the purposes and entities listed in this notice are saved and made available to those entities in the form of digital signals (such as a string of characters). This is necessary in order to enable both this service and those entities to respect such choices.
Non-TCF/GVL Vendors
have your say