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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
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No better time to make the plunge and get an android phone. Equivalent hardware spec for a fraction of the price.
@Random_paddy: and far less restrictions.
@Random_paddy: Equivalent hardware does not mean equivalent performance. There will always be a performance benefit for software designed around a known range of proprietary hardware compared to an Android OS which needs to be able to operate with every sort of ram, processor and core combination under the sun.
@Random_paddy: Not really about the hardware, the Apple ecosystem works too well when you have more than one of their devices.
Also, if you know how to use a screwdriver you can replace your own battery in less than 10 mins.
So many, more useful, apps available on Android. I wouldn’t go back to using less myself.
@Rochelle: And thats why major manufacturers all optimise the opreating system specifically to the phone’s model.
But apart from android vs iOS apple is not an ethical company and should not be supported.
So they “do anything to intentionally shorten the life of any Apple product”! But they then admit to slowing down apps to increase the life of the product. If that happens to result in their customers being pushed to buy their latest product at their usual vastly inflated price, all the better. They really are such a soulless, money grabbing, tax dodging bunch of creeps. The Apple is rotten to the core.
@Fake Avast: Not too sure I follow that logic to be honest..
No such joy in Ireland. It’s €89 plus €12.30 shipping here.
https://support.apple.com/en-ie/iphone/repair/service/pricing
@Jesus Christ: They’re going to change it to €234 from the end of January
@Jesus Christ: The article says starting late January.
@Peter: probably wont apply in Ireland as no lawsuit is in effect against Apple here
@Liam Burke: €10 on eBay.
I’ve an iPhone 6 and it sometimes shuts down for no reason in the midd
You know that when a company like Apple apologize that what they say in their apology is the exact opposite of what they have been doing.
@David Stapleton:
So are you saying that Apple actually made older phones operate faster with the s/w release? Please explain what they are doing which is the opposite of what they are saying
@Nick Allen: hahaha, is this an exam?
@David Stapleton: I figured that out when I saw all the global user and tech groups have been requesting this improvement for years, yet it took lawsuits to achieve the offer of one new battery.
Have to say my iPhone 6 is the best phone I’ve ever had. Not surprised they wanted to slow them down because no one is upgrading.
@mcgoo: Every company tried that on. And compromised. Finally Apple users have something similar, good, I suppose.
The fact that it cost €66 euro for a replacement is a disgrace and I’ve heard of places more expensive
@Del Haven:
What point are you making in sharing that you have already heard of place more expensive?
@Nick Allen: In the big people’s story above it says €66. Jesus Christ himself even said it was more expensive in the comments. What point are you making in sharing that you’re inquisitive about my “place more expensive” post?
@Nick Allen:
Out the wrong side of the beddy boos again today Nickie?
@Tweed Cap: everyone screws the Irish. We have a reputation for paying it. Everyone charges us double
@Tweed Cap: no he’s just a gobshîte, the sooner people ignore him, the quicker he’ll go away.
If you buy apple your a fool simple, even people working in apple would tell you that..
@Lad: care to explain please ?
@Lad: A handy thing about Apple devices is their built-in spell checker. Keeps a user from looking too ignorant. Unfortunately it doesn’t help if someone can’t tell the difference between ‘your’ and ‘you’re’ when doing their daily round of trolling …
@blorp: that’s a deep burn there
@Lad: agreed.
If you have a wallet that is too heavy in your pocket. Apple will gladly lighten it and award you with the new iPhone X. You will cordially be invited to join the queue outside for the next iPhone launch at an apple store near you . Launch date next September.
Don’t forget your sleeping bag and and raincoat.
Almost forgot, bring a thick wallet.
Where’s the APPLE CEO in all of this. Burying his head in the sand. Not good news so I take a vacation and someone else can take the flak. Who does the work on replacing battery. If they update to monitor the battery then they control numbers requiring replacement. Why don’t they just replace all batteries
I bought my first iPhone 2 years ago, the 5s and the same thing happened started to go off on its own with 30% charge on it, just shortly after an update, next year the same with the 6 and now I have a 7 and low and behold the same is happening with this after the I updated to the OS install 10, well as if I wasn’t already p!zzed off about the price hike, 32gb minimum memory withdrawn (32gb) on the 8 (it only came out last year ffs, as if that that didn’t tell you enough about their marketing strategy of forcing you to upgrade. What a joke, should have listened to my pal who told me phone technicians have suspected this was going on for some time, never again will I buy an Apple product. Back to Samsung for me. Rotten Apples
If you are that upset when it comes to upgrading get an Android .
Isn’t it fascinating how strongly people feel about technology products, Xbox vs Playstation, PC vs Mac, iPhone vs Android, Spotify vs Apple Music, Samsung vs LG.
It achieves nothing but bolster both companies, yet the fight will continue to go on.
I was onto them weeks ago about this, made me out to be liar, stupid thinking a iPhone would last longer than two years without replacement parts.
How will this all sit with our consumer laws? They’ve admitted a problem.
@GizmoIrl: I have a HTC since 2014 and it’s still going strong.
@Fiona Fitzgerald: I might be moving Apple support gone down last few years
Planned (built in) obsolescence
https://en.wikipedia.org/wiki/Planned_obsolescence
Filthy shysters.
Not surprised. The vast majority of their profits are made in the iPhone so do this to keep the ball rolling in terms of profit increases.
I love my IPhone but even in the new phone , the batteries are so poor. Apple needs to seriously work to improve battery life if it wants to stay ahead.
@IrishLiberal: Everyone wants a new generation of battery technology. They could do a lot more to optimise software performance until that leap happens. Takes a lot of consumer demand to push back and have that available. HTC did this – held out for a few years to sell more phones. Eventually they caught on that people were just not into buying a new one every year or two, that it was a global trend, so HTC released a great upgrade that made the most of the phones we had. Memory and power were optimised so that we didn’t need to change phones. They got it. Now Apple is seeing the light, a bit more slowly. It’s something.
iPhones are definitely a good phone, but……
I’ve always had them, currently have a 6 and considering making the jump to Android, maybe a Sony Xperia ZX1 compact. Just replaced the battery in the 6; you can get it done in any phone repair shop for around €50. That’ll buy me another year at least if I wanted to keep it. The reason I’ll be switching is the eventual battery & charging issues that have happened after a couple of years with this & the last 2 iPhones. Does it happen with Androids? Not as much I’m told, but I don’t know.
@Derek Peyton: That’s my priority too. Not if you shop around for the best battery currently available. mAh (milli-Ampere-hours) is what you need to look for in the phone spec. Go for a replaceable one with mAh over 10,000. Ideally fast-charging too. Maybe buy a spare battery when you buy your phone, so they can’t tell you it’s been discontinued years later. I think we’re all waiting for a leap forward in battery technology TBH. Software only minimises how much power our apps use – the battery life is the current sticking point. It’s like memory – that used to limit our options. Now memory’s cheaper and power is the issue because we all use them more and connect more.
@Derek Peyton: got my first iPhone this year, work phone! Nothing but trouble, turning off, freezing and the charger connection not working and I have to jimmy it a certain way to charge! Plus the fact the phone is just stupid to use. Nothing stands out for me problem wise with the Samsungs and HTC’s Ive had.
And what about those of us who already had to fork out for a replacement battery locally because the iOS11 update completely consumed my battery rendering the phone unusable!? Had no option but to have it replaced locally as Apple were giving me the runaround, apparently waiting for technicians to look at my case. Then the phone battery completely died.
I won’t buy another Apple product now, totally done with them.
I have never updated my IOS version to 11!! Firstly because I didn’t like the new layout and secondly I would wait to see if there are issues with the update!! Glad I didn’t as my iPhone 6s !! Is running with out problems!! While others are complaining their phones have become very slow!! I was surprised to find that people couldn’t roll back to the previous OS!!! I wonder why???
@Julesy: You could update to 11.2 now without any issue, the initial releases had bugs that were worked out. The power management software was introduced a year ago in 10.2.1, so you are most likely currently using it, but you won’t notice anything until your battery starts to naturally degrade.
@Julesy: It’s called backward compatibility. Newer software companies ignore it to push people to upgrade and spend more. If you force upgrades, you can get companies to buy newer faster hardware too. Eventually they have to lease it instead of buying.
@Julesy: don’t do it!!! The iOS11 update totally fried my battery. Hadn’t an issue with it prior to the update. Had to have it replaced as the phone wouldn’t hold charge even when connected to the charger!
It’s never fails to amaze me that android users will actually take time out of their day to comment on articles related to Apple. Bizarre but funny to see them foaming at the mouth.
The same people all tricked by the clever marketing of Samsung , HTC and Huawei etc believing that filler specs on paper equals a great user experience actually call iPhone users sheep haha!! A phone can have the best camera, screen and Memory but it’s always bogged by the utterly atrocious android OS . How people can pay hundreds of euro for phone running a generic OS across brands is beyond me. By at least it’s water proof :)
Aw. Great bunch of lads, Apple.
But giving you a new battery at a discounted price doesn’t fix the slow down software!
It should be , new software released to allow old phones run at normal speed + new discounted battery as an apology
My 5s is only a year old since last august & now keeps shutting down even if the battery is 40% been told its a software issue with apple which is costly to fix.. turned me right off Apple products & now looking to get a good Android that doesn’t cost an arm & a leg…
I’ll keep it short. Iphones are shit.
Most of these apple comments lack byte!!!!
I would love to be able to decide what part of updates I want to install, e.g, only opt in to security updates.
What about iPhone5, it too has the same issues? Hope the battery can be replaced with discounted price.
have your say