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THIS HAS BEEN Maths Week and if you’ve clicked in here, you are likely to have been puzzling over our fiendish maths challenges on TheJournal.ie all week.
So let’s not delay further: these are the answers you’ve been waiting for.
Let us know how you did in the comments…
Monday: The One With The Old Library Book Fines.
The answer: It would make a considerable dent in your inheritance. The fine due this week would be over €112 million – that is IR£88 million.
The method:
Compound interest is calculated as follows: A = P(1+I) n
It will be obvious that adding interest after every week causes the amount to increase rapidly. A lot of people are caught out by seeming small interest rates but compounded over short intervals. It may be of little significance if paid off quickly but if left may accrue rapidly.
Tuesday: The One With The Poles Along A Road.
The answer: 9km/h
The method:
There are 10 poles and you run from 1 st to 10 th – that is 9 intervals which is 450m.
Speed is distance/time (we want the answer in km/h so it is convenient now to convert to km and hours)
450m is 0.45km. 3 minutes is 1/20 of an hour.
Speed is therefore is 0.45/(1/20) = 0.45 x 20 = 9 km/h
Wednesday: The One With The Four-Digit Number.
The answer: 3636
The method:
Assign the symbols w,x,y,z for the digits
Thursday: The One Where Two Cars Pass Through Toll Booths.
The answer: 135km apart
The method:
(It might be easier to think of two cars passing each other – how far apart would they be in 36 mins – this is an equivalent question)
They are driving towards each other at a rate of 115 + 110 = 225 km/h
Speed = distance/time
So distance = speed x time
36 mins = 36/60 hours =0.6 hours
Distance = 225 x 0.6 = 135 km
Friday’s Question: The One Where Two Kayakers Paddle On The Liffey.
The answer: Kayaker A. Kayaker B can only manage 6km/h in still water.
The method:
Kayaker A with an effort that would transport him at 9 km/h in still water against a current of 5 km/h can only manage 4 km/h.
Kayaker B is assisted by the current and will be travelling 5km/h faster than his normal ability.
We must calculate how far A gets in 10 minutes. (1/6 hour)
At 4km/h in 1/6 h, he will travel 4 x 1/6 = 4/6 km
Kayaker B will therefore have travelled a distance of (2.5 – 4/6) km in 10 minutes
Which will be: (2.5 – 4/6)/(1/6) = 11 km/h
If Kayaker B is doing 11 km/h assisted by the 5km/h current then his ability on still water is 6km/h.
Saturday morning: The One With The Tombola Tickets.
The answer: 63: 4 ending in 0, 14 ending in 5, 24 ending in 1 and 21 others.
The method: Look for useful information in question and express it in equations –
Two out of three chances of winning gives us: 3(A+B+C) = 2(A + B + C + D) (1)
If you bought 60 tickets you would be sure of winning a bottle of brandy – therefore there are 59 tickets that are not brandy. B+C+D =59 (2)
For the others:
Add these three equations:
and we get: 2A + 2B + 2C + 3D = 147 (5)
But equation (1) tells us: 3(A+B+C) = 2(A + B + C + D) (1)
Multiplying out: 3A+3B+3C=2A+2B+2C+2D
Which reduces to: A+B+C =2D
Which when multiplied by 2 becomes: 2A + 2B + 2C = 4D (6)
Recalling that (5): 2A + 2B + 2C + 3D = 147 (5)
Substituting (6) into (5) gives us: 7D = 147
So that gives D – the number of non-winning tickets: D = 21
Substituting in this value into equations (2) (3) and (4):
Subtracting (8) from (7) gives: B-A=10 (10)
Adding (10) to (9) gives: 2B = 28
Saturday evening: The One With The 3-D Puzzles
Answer…
Part one: B – Cannot be folded into a cube
Part two: Playing Die – A=3, B=6, C=2
Vicky Phelan has been a true hero in all of this, but I think now it’s time to leave her & her family alone & leave them in peace give them privacy & let Vicky get the best possible treatment ,plenty of rest & relaxation. Wishing them lots of love x
@Colette Kearns: well and feelingly said. She exposed the terrible mess. Now it is for others to fix it.
Dr. Anthony O’Connor this is the first article I have ever read in any Irish Newspaper since my return to Ireland 2 years ago that has struck me as totally sincere and provides for a reader a precise view of the real issues and obstacles that Health Care in Ireland face. Intentions and Plans seem good but Implementation is poor as you say, I see it every day as a cancer patient myself Brillant Staff but not enough of them and rushed off their feet working in antiquated facilities in corridors less than 1meter wide and only 50% of the beds needed for the chemo patients in the waiting room that day.
Your comments on the media 100% correct
Your comments on the seemingly outraged politicians 100% correct and struck me over the last days also as totally IMMORAL have they worked in Heath Care any of them what gives them the right to call for heads to roll they are themselves totally unaccountable to anyone.
Only outrage of interest to me and I believe many others in Ireland is the outrage of the victims thank you for expressing this view and all others and for your work in Health Care Ireland.
@Teresa: I have to agree, if i could applaud I would. A few months ago my family an I were in our local A&E Department with my elderly mother, the curse of aging, while there we had the privilige of meeting a young nurse who basically advocated for my mother. We were, frankly out of our depth and comfort zone while she knew how to navigate the mine field that is a modern hospital.
On the night we came in she came to check my mother and, for no reason, was obviously upset and crying. She apologised profusely and explained that they’d just diagnosed a young man with some sort of advanced brain cancer, he was terminal and had little time left. She was both hurt and angry that he would have to be diagnosed with such a condition in an A&E Department, and he was the fourth that week.
I can’t help but feel this may be the tip of the iceberg, what happens if the same thing occurs with colorectal cancer, breast cancer, etc. If major cancer diagnoses are being made in A&E Departments it should have been a warning signal that we already had a significant problem. Either nobody was listening or this was ignored. We’re at a crossroads now, we can decide to blunder on, doing as we’ve always done, or we can listen to experts, leave the politics aside and invest in our healthcare.
@Teresa: yes he nailed the real Ireland and absolutely lack of talent our politicians contain all they have done in the past week is to out do each other in shock and horror responses.
Great article. We lash money at systems, and then put people in charge who can’t use them properly or couldn’t be bothered. Proper oversight is vital.
@Nick Caffrey: I think Nick proper accountability is most important. These people should know before they are appointed that they will be held accountable for their actions or lack of. We cannot have a system where those responsible can wash their hands of the outcome & walk away into the west with a huge pension & golden handshake
@Ciaran Kehoe: silence is no good heads should be rolling. Media shoot report this but they being silent.
I have yet to see a response from the HSE (or, indeed, any government agency) that outlines in clear language, what happened, who was in charge when it did, and what action was taken.
Poor FFG political elite outraged :-(
Penny pinching to pay a debt not ours for a mega Europe is essentially to blame.
Yet not another cent is outraged..
@Willy Malone:the killers of Jean Mc Conville are outraged
Not the first time he gave an incisive look and informed comment on the health service and its failings.
He sounds like he should either be the minister for health, or the head of the HSE.
My mother died of cervical cancer in 2016, looking back through her records she was previously diagnosed with an abnormal smear at cin3 stage and it was noted that invasion could not be ruled out. She was given the all clear 6 months later but continued to have all the symptoms of cervical cancer. She was in hospital and seeing doctors with her symptoms almost on a weekly basis, I can’t for the life of me understand how all those hospital visits could not pick up on this cancer until it was too late, given her history.
Good article but I would have preferred to read a set of specific fixing measures.
The priority is to fix this crisis.
Adopting superior HPV testing makes sense.
Annual screening makes sense.
Retesting as a matter of priority women between the age of 20 and 60 makes sense.
HPV vaccination all boys and girls to achieve 95% herd immunity level makes sense.
@Michael Lang: he’s a gastroenterologist not an obstetrician/gynaecologist, expecting specific recommendations from him is like asking an electrician to fix a persistently clogged toilet, both in a house but totally different specialties. What I believe he is trying to express is having finite control/regulations over doctors and nurses isn’t going to change anything unless they work in a system that functions and that there is accountability in management, not the usual ‘god that’s awful, how did that ever happen? I was never made aware of that’ comments that seem to be on an endless loop these days
@daveyt: he should know enough general medicine to point to the very obvious and necessary fixes required.
The relevant speciality is oncology but it plainly obvious what needs to be done to fix this problem.
@Michael Lang:I’m sure he does know Micheal but chose to concentrate on what he did focus on in order for it to have maximum effect. And it worked.It’s called the art of essay writing. He stripped to the bare essentials the reasons this problem keeps happening. In my opinion the main point he was making was until people start genuinely putting health care high on the totem pole of why to vote for which candidate health care will be ignored. The economy and taxes or immigration being priorities in peoples minds when it comes to polling day does not this mess fix. Politicians and civil servants tend to get their arse in to gear when their power is threatened. The specifics of solutions is a different essay that would have made the key points of this essay obscured.
@Michael Lang: We should be basing our decisions on sound medical evidence and expert opinion, not on intuitions and emotions.
Overpopulated management levels in H.S.E, huge civil service , who you know ,not what you know promotions leading to incompetence ,when all these salaries have been paid not a lot left for actual services.
Dr O’Connor – at long last, a voice which transcends the accepted societal norm of political points scoring and truly elevates this, and other tragedies, to questioning what we need or want our health service, or indeed any other public service to be, is it actually achievable and how are expectations managed. Society has changed immensely in such a short time. Time to reinvent the wheel ? – perhaps, or look at what works well in other countries, why and how. If we continue to patch up and focus on our own failings, we’ll achieve nothing except distraction.
Brilliant clear article. We need a national health system with national standards and regular audit of those systems. Unfortunately we have no national standards just local ad-hoc arrangements where the organisation is responsible but no individual person stands ultimately accountable.
CEOs of companies are accountable; so should the head of the HSE and the minister be.
@Kevin Slater: I have a relative who runs a very expensive and exclusive creche, it’s audited and inspected severaltimes per year, for the slightest infraction they get a warning. If this isn’t corrected tot he satisfaction of whoever happens to be carrying out the relevant inspection they’ll be closed.
However while the HSE carry out such inspections and have the power to close premises, and have done, they themselves aren’t subject to the same rules, standards and accountability the hold others to.
Spot on willy and this should be rammed down their throats leading up to the next election.
The outrage expressed by F.G. and supported by F.F. under whose tenure the testing of cervical cancer was farmed out to the lowest bidder is beyond belief. History repeating itself..Who remembers Michael Noonan dragging sick and terminally ill people though the courts concerning the blood transfusion scandal. Not making a political point as I usually would do, but how long before the next scandal props up.
It’s showing them up to be a real bunch of clueless amateurs.
Ivan Yates was even telling harris what to do yesterday. Ie: put a board in place for the HSE and set up a redress scheme. Problem is amateur harris has no experience or qualification in running a large organization.
@Adrian:Ivan, his company went bankrupt,so he should be telling people how to run things ,yeah right
@Robert Harris: you learn from your mistakes and I would say yates is imminently more competent than all gov ministers at this stage. Harris is calling for SMITs, and scoping exercises and commissions of enquiry and talking about memos and whatever buzz words he can think of, but behind it all, he’s showing himself up to be very amateurish, incompetent and clueless in dealing with the issue. (Just as lost as creed was weeks ago with the fodder crisis)
You have said what every right minded person is thinking. Well done.
Anthony o connor ,we need to get everyone round the table ,unions ,consultants ,management ,ministers and of course the legal profession .we need a transparent code of practice which will be open to public scrutiny and an independent outside assessment …we can talk to the cows come home and not much will change .i have even heard through the grapevine that other screenings related to other medical issues may well need to be examined ,this may well be political dynamite .we have some of the best paid politicians in the world ,best paid consultants and best paid management and the legal profession are out on their own .its time they all stood up for the citizens of Ireland or get out of the way .radical change is needed and it NOW
Michael Noonan was a specialist in that field ,and we have the makings of another specialist
Oh yes at least someone tells the politicians were to get off their high horses
Great article. I too feel frustrated and angry about the ‘posturing’ of politicians. being indignant, disgusted, angry is not what we need. we need a root & branch cultural change about how the medical profession perceive women. As a woman, sick and disabled, in Irish hospitals I’ve been shouted at, dismissed, with male doctors walking out of the room if I question, challenge or ask for more tests. I’ve had my medical files slammed on the table, I’ve had frosty cold angry stares and have had diagnosis dismissed.
Hey ho; what do I do? I get myself to the UK under the E112, get the tests I needed, get a proper diagnosis (a very rare neuro-muscular degenerative disease) after muscles biopsies, various neuro-muscular electrical/scientific tests, Highly sophisticated technology at the disposal of these (two) high powered centres of neurological excellence, not available in Ireland, not even Beaumont, and I get DIAGNOSED. Return to Ireland and the doctors dismiss it. I kid you not.
Now I’m telling you its arrogance, misogyny , disrespect, and women seen as ‘hysterical’, with ‘somatoform’ written on the files, and the utter arrogance of dismissing women’s concerns medically that’s killing us.
This scandal has roots, the roots are ‘women’s health is not priority’. The medical culture towards female patients is sometimes little more than disguised contempt. Even female hatred. Because women who challenge, complain, argue, or ask of consultants are not LIKED. why?
Because many of our male consultants still think they know everything, are Gods, experts & are as arrogant as hell. They operate under “if I don’t know it/ understand it – it doesn’t exist”.
This scandal was not ‘picked up’ by the medical profession – it was exposed by a woman who was , lets not beat about the bush – let die to save institutions, medics and vested powerful interests. She and all the others who have died were sacrificed to ‘cover-up’ the institutions negligence.
Varadkar & Harris can ‘posture’ to kingdom come but as men do they really LISTEN to women.
As a ‘failed’ woman medically I’ve asked to meet Simon Harris, my constituency TD, (Greystones) no reply, no meeting, no nothing…Aaaaahhhhh This woman is very angry indeed.
My solution, a hospital for women, run by & for women. Get me away from misogyny in the medical profession. toxic and killing women.
Even the usual fake pro gov profiles are unusually quiet on this one. If it wasn’t for Vicky Philanthropy how many more women would Vradkar and Co let die? They should hang their heads in shame, better still,there should be a criminal investigation.
@Ben Dunne: whoops.Meant Phelan.
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