Tuesday Tangles (and Answers)

What is Tuesday Tangle?

The Tangles were prompted by some sad news: a friend's father was recently diagnosed with Alzheimer’s Syndrome. Alzheimer’s is a form of senile dementia, which affects about 26 million people sufferers world-wide. At present it is incurable; however, it is possible to decrease your chance of being affected. The key is keeping your mind active throughout your life, whether by trying new experiences, learning a second language, reading widely, travel, and anything else which challenges the grey matter.

With this is mind, I decided I’d start the Tuesday Tangle: every Tuesday, I will post a logical brain-teaser. On Wednesday I will post the correct answer (with an explanation of how to get there). In this small way I hope to stimulate your grey matter... or at least help you to procrastinate from writing :)

Tuesday Tangles will be posted on the main page of the blog, but here you will find an archive of all the Tangles. 


Tuesday's Tangle, 22nd March 2011:

this week's Tangle is my publishing-obsessed twist on an old favourite. See if you can figure it out (and if you remember the original):

You are a literary agent, whose author client has written a fabulous new novel, a massive hardcover tome of two thousand pages. 

Tonight is the novel's launch party, across town. You need to bring with you the author, the novel, and your annoying cousin who happens to be a very scathing book critic. However, all you have for transport is your aging (but tres chic) Vespa, so you can carry only one thing with you at a time (the author, the novel, or the critic). 

BUT if you leave the author alone with the critic, there will be fireworks. If you leave the critic alone with the book, he'll rip it to pieces. How do you get all three to the book launch, with the minimal amount of damage?  

Solution:  (Mouse over to reveal)

Lucky you're on a Vespa, because otherwise this would cost you a lot in gas!

First, take your annoying cousin (the critic) to the party. Return home to pick up the novel, then take the novel to the party.

At the party, pick up your annoying cousin the critic (they're probably sick of him anyway), and bring him back with you to your apartment.  Drop the critic off, pick up your author client, and take him to the party across town.

Then (if you really have to) return to your apartment and pick up your annoying cousin.

So, how did you do? Do you have what it takes to be a literary agent? ;)

PS I'd just like to say to any critics reading this blog, that I think literary critics are the salt of the earth. Really. They make the literary world go round. So please don't mess with my stuff.

Tuesday's Tangle 14th February 2011:

This week's tangle is dedicated to the amazing strength of will that stopped me from succumbing to an infomercial yesterday. Said infomercial featured the *amazing* Ab-Circle Pro. They were on special! Everyone on the ad was so thin! And they promised me masses of weight loss in just three minutes a day. Three minutes a day. Heck, even I have that kind of time lying around. 

However, just as I was reaching for the phone, the rational side of my brain spoke up (which was a damn-near miracle, since I could swear I'd left it chained to a radiator somewhere). So, long story short: I'm still as flabby as ever, but I'm loving that bonus three minutes a day that I don't have to exercise.

And what did I use today's three minutes for? Why, to furnish you with this week's tangle, of course...

Lose Ten Brain Cells in Nine Minutes!

Tanya is a sucker for TV infomercials. Her latest purchase is an exercise machine which, the sellers claim, will enable her to lose 10 pounds in one week. All she needs to do - so they say - is use the machine for nine continuous minutes each day.

On the first day, an enthusiastic Tanya throws on her track pants and searches the house for a timer. But all she can find is two old fashioned egg timers. The smaller egg timer takes four minutes for the sand to go through, while the bigger takes seven minutes for the sand to go through.

If Tanya cannot stop or slow down the sand while it is falling through the egg timers, how can she know when she has been exercising for nine minutes? (Presume that Tanya is able to flip the egg timer without getting off the machine, so it doesn’t interrupt her exercise.)

Solution (Mouse over to reveal): Tanya starts both egg timers at the same time, and begins exercising.

At the four-minute mark she turns the smaller egg timer over. She has been exercising for four minutes.

At the seven minute mark, she turns the large egg timer over. She has now been  exercising for seven minutes.

At the eight minute mark, the small egg timer needs turning. But instead, Tanya turns over the large egg timer. Because it had been running for only one minute, when she turns it over, the sand in the large egg timer runs for exactly another minute in the other direction. At the end of this minute, when the large egg timer is finished, Tanya has been exercising for nine minutes.

Tuesday’s Tangle 25th January 2011:

This Tangle doesn’t involve any mathematics, but does require lateral thinking (I was hopeless at it, but Handsome Husband triumphed). I’ve included the answer in today’s post, for those who just can’t wait until tomorrow.

While renovating a house, Meryl discovers three light switches, side by side, on the second floor. When she asks the builder what the switches are for, she learns they control the three bare bulbs that hang in the attic, one floor above. He can’t, however, tell her which bulb is controlled by which switch.

Meryl, being lazy, wants to climb the attic stairs as few times as possible to solve the mystery. Is there a way she can determine which light switch controls each light bulb, with only ONE TRIP up to the attic?

Solution (roll over with mouse to reveal): Yes, there is a way she can do it with only one trip to the attic. 

Let’s call the switches A, B and C. Meryl switches on light switch A, and leaves it on for five minutes. After five minutes, she switches A off, and switches on B.

Then she goes up to the attic. The bulb which is lit is obviously controlled by switch B. If Meryl touches the remaining two (unlit) bulbs, one will be warm and one will be cold. The warm one is then controlled by switch A, and the cold one by switch C.

Tuesday’s Tangle 18th January 2011:

Selene Deon is a budding songstress in the town of Erewhon. Last December she put on two concerts in the Erewhon town hall.

The first concert, on Saturday, had a ticket price of $10 for the first three rows, and a ticket price of $6 for every other seat.

The Saturday concert was a sell-out, and the takings were $2040 for the night.

Being a bit of a diva, Selene decided to raise the ticket prices for the second concert, on Sunday. This time, the first four rows were charged at $10 per ticket. Every other seat was $6.

Again, every seat sold. Sunday’s takings were $2120.

If all the rows had exactly the same amount of seats, can you work out how many seats there were in the Erewhon town hall?

Hint: (roll over this holding down the mouse button to reveal the Hint) first work out the difference in takings from Saturday to Sunday. This extra money must represent the ticket price increase, which we know equals $4 extra, for every seat in the fourth row. The ticket prices in all the other rows remained the same.

Solution (Mouse over to reveal):

To find the amount of seats in the Erewhon Town Hall for Selene's concert, we must first work out the difference in takings from Saturday to Sunday. This extra money must represent the ticket price increase, which we know equals $4 extra, for every seat in the fourth row. The ticket prices in all the other rows remained the same.

We know that the difference in takings from Saturday to Sunday is $80. This extra profit represents the additional money gained for Row Four. The first night, Row Four was only $6 per seat, and the second night it was $10 per seat. Taking this into account, we know that Row Four brought it an extra $4 per seat.

So, we take the extra profit ($80) and divide it by the profit per seat in Row Four ($4). This gives us 20, which is therefore the number of seats in Row Four.

We know that all rows had the same number of seats, so therefore each row had 20 seats.

Now we must work out how many seats there were in total.

We know that, on Sunday, there were four rows with 20 seats (totalling 80), which charged $10 each. Therefore Selene got $800 from these seats.

Deducting $800 from the overall takings of Sunday night (which was $2120), we get $1320. This represents the takings from all the other seats (Row five and backwards). 

If we divide the takings from Row Five and backwards, $1320, by the ticket price, $6, we get 220. This is the number of seats there are from Row Five and backwards.

Therefore, we have 80 seats in the first four rows, and 220 seats in the rest of the hall. This means that there were 300 seats (and 15 rows) in total in the Erewhon Town Hall for Selene’s concerts.