Things we should really be afraid of

This monthly calendar of hazards is provided as a public service. Print this out and locate it in a prominent place in your bedroom. Check the list each morning before you get up, so you know what to watch out for on that day.

Only trust this: you know you can, because you read it on the internet.

1^st. Today, if you go outside, you will be repeatedly struck by air molecules travelling at more than the speed of sound. The bad news is that the same thing will happen, even if you stay inside the house. You are doomed.

2^nd. You will probably ingest millions of molecules of dihydrogen oxide today. This stuff reacts with sodium, which is found in sodium chloride, so do not touch the salt shaker.

3^rd. Today, there will be in excess of 40 lightning strikes per second, all day and all night. Best to stay inside, and if you go outside, do not raise your hand. To be extra sure, drag your knuckles on the ground.

4^th. In an area 100 metres square, there will be between 3 and 4 kg of birds on average, equal to two frozen chickens. Consider that these are live birds, which must die and fall at some point. There is a risk that you could be hit on the head by something with twice the mass of a frozen chicken today. Stay inside.

5^th. The energy you use in climbing two flights of stairs is enough to ignite a glass of brandy. Do not climb upstairs after drinking. Lie on the floor, and remain completely still. Stay there until midnight.

6^th. Most people die within 24 hours of their last meal involving a dead animal. The rest have nearly all eaten dead plants, so do the sums. Do not eat today.

7^th. When a large earthquake hits, you will probably have less than 10 seconds to get to safety. Keep up your training.

8^th. Today, there will be 100 tons of meteor material striking the Earth. Carry an umbrella at all times today.

9^th. Avoid contact with people, today and every day. The average human body contains 115 grams of toxic chlorine.

10^th. On this day, there will be at least four earthquakes with a magnitude greater than 5.0. Do not venture out without a tinfoil hat.

11^th. At some point today, you will find yourself coming under the influence of the moon’s gravitational field. Make sure that you hang onto banisters and railings at all time, and wear heavy boots.

12^th. There will be quite a few mites living on your forehead. If you are outnumbered by your Demodex folliculorum, you might as well start making your last will and testament. Tomorrow will be too late.

13^th. Any day which has a 13 in it is also a day on which the mathematical statement 6x9=42 is correct, in base-13 notation. Such a day is not a good day for doing anything that involves numbers: no taxation returns, and do not issue or pay bills.

14^th. Today is probably a good day to consider that dried fruits (and especially sun-dried tomatoes) are all examples of irradiated foods. Be very wary of currant buns.

15^th. Today is the Ides of this month. If Julius Caesar had offspring, you probably have him as an ancestor, and that leaves you at risk.

16^th. In all probability, your food today will contain genes, and some of these will be mutated. You may as well just give up now.

17^th. Statistics show that more people die in the average hospital than die in the average home. Stay away from hospitals all day.

18^th. Did you know that your computer emits the same frequencies of visible radiation that come from nuclear explosions? Be very nervous of computers today.

19^th. Take careful note of the old people around you, and you will see that they are more likely to wear glasses and carry sticks. This indicates a possible cause of aging that should not be ignored.

20^th. Every time you read a book, you will be exposed to visible spectrum radiation.

21^st. This is the only day in the month when genuine rich Nigerians send out their offers of money, so while you need to be fearful on every other day of the month, you will be safe responding to emails from Nigeria sent on this day.

22^nd. The air that you breathe contains radon, a radioactive gas. There is only one way to avoid this, which is to stop breathing. Do this all day.

23^rd. In an area 100 metres square, there will be about 160 kg of spiders, insects and germs. Wear protective footwear at all times.

24^th. Statistics show that most people who are murdered are killed by people who have recently been exposed to visible radiation. Do not go out until it gets dark.

25^th. Avoid approaching live birds and mammals (including humans) because they all emit thermal radiation, similar to that which comes from bushfires.

26^th. This is the only day in the month when ninjas are visible on the roads, but only when you shut your eyes. This is safe: they are in black helicopter, so you won’t hit them.

27^th. Towards the end of each month, people start sending more emails in bold, and this uses fat ASCII codes, which can get jammed in the wires and stuff. Do not leave the house today without running a vacuum cleaner over your mouse and keyboard.

28^th. Potatoes are poisonous, and eating as little as 200 kg could kill you. Your only hope is that a plague of snails comes through and takes out the potatoes.

29^th. Research shows that most people your age have many different germs living in their intestines.

30^th. Church bells, door bells and cow bells are all tocsic.

31^st. Note that 31 is 13 backwards, and brace yourself. This is the day in the month on which unexpected things happen: worms turn, uncounted chickens come home to roast and to prepare for the 4^th of next month. Do not read your horoscope today, because it will contain information that will mean that the government will have to kill you (and you can't see the ninjas today). Stay in bed, but be aware that quite a large number of people die in a bed each year. Are you feeling lucky?

General note that I am adding to some of my blog entries: I have lots of different interests. If some area interests you, look at the very end and you will see a set of tags called labels. These are hot links that will give you a list of other articles with the same tag/label.

Solving logic problems

Allen, Bruce, Claire, Donna, and Emma were the top five finishers in their school's talent contest. They finished up filling, in no particular order, 1st, 2nd, 3rd, 4th, and 5th places. Oddly enough, the children came from, in no particular order, 1st, 2nd, 3rd, 4th, and 5th grades! In another startling coincidence, they all performed to the song "My Way" but they all did something different to the music. They either hummed, sang, tap-danced, whistled or yodelled.

Based on the clues, match names with order of finish, grades, and performances.

   1. none of the numbers in the order of finish were exactly the same as the grade numbers.

   2. Claire finished in front of Allen but behind the singer, and Donna, and the tap-dancer too, but those last three people are not necessarily in any particular order.

   3. Emma finished behind Bruce but ahead of Donna.

   4. the singer was in 3rd grade and the tap dancer was in 1st grade.

   5. the child that was the hummer deserved to finish in last place and did finish there.

   6. the yodeller was in 4th grade.

Your task: to try and work out who came where.

 First, we need to work out what the variables are that we have to slot in, We have the names, ABCDE, we have the grades, 12345, and the places 12345, and the performances, hstwy. Now we are ready to begin.

The trick is to draw up a table, and then begin eliminating the impossibles. To give you a start, I have applied two statements: you can carry on from there.

After applying statement 1:

Place	1	2	3	4	5
Grade	2345	1345	1245	1235	1234
Name	ABCDE	ABCDE	ABCDE	ABCDE	ABCDE
Performance	hstwy	hstwy	hstwy	hstwy	hstwy

 After applying statement 2:

Place	1	2	3	4	5
Grade	2345	1345	1245	1235	1234
Name	BDE	BDE	BDE	C	A
Performance	hstwy	hstwy	hstwy	hwy	hwy

 After applying statement 3:

Place	1	2	3	4	5
Grade	2345	1345	1245	1235	1234
Name	B	E	D	C	A
Performance	hstwy	hstwy	hstwy	hwy	hwy

 Now go back an apply statement 2 again...

From here, you're on your own :-)

General note that I am adding to some of my blog entries: I have lots of different interests. If some area interests you, look at the very end and you will see a set of tags called labels. These are hot links that will give you a list of other articles with the same tag/label.

Adventures with 1729

Talking of cubes as I was in my last post, even when people are thinking about the same thing, they are probably thinking in different ways. A famous English mathematician called Hardy once visited a very clever Indian mathematician called Ramanujan in hospital.

He probably wanted to know if Ramanujan had discovered a curious set of numbers called Carmichael numbers, so Hardy said casually that he had travelled there in a taxi with a boring number, 1729.

Ramanujan sat up in bed. "Oh no, Hardy, on the contrary, that is a very interesting number. It is the first number which is the sum of two cubes in two different ways!"

When Hardy thought it through, he realised that 1729 was the sum of 9 cubed and 10 cubed (729 + 1000), or of 12 cubed and 1 cubed (1728 + 1). When I came across this story, I noticed something much less interesting: 1729 is the product of three prime numbers which are in mathematical progression (7 x 13 x 19) -- I guess I am just a bit boring where numbers go.

One day, I had an idea for a problem: using just the numbers 1, 7, 2 and 9, in that order, and using any mathematical notation, I set out to see how many different numbers I could get.  I began with trial and error, a good old-fashioned method that has always served humanity well.  Bang the rocks together, notice what makes useful flakes, and bang them again, that sort of thing.

That got me a few answers, like 1 = 1^729, or 1 = 1 + 7 + 2 - 9 or 6 = 1 + (7x2) -9 but then I began running out of new numbers.  Then I switched to the sort of clever trick that is used when pharmacists take drugs that work, and fiddle with them, changing the bits systematically.

You can find some hints by poking around in this area. DO look around, or you will miss some important stuff.

 

Then we could turn to the problem that I will describe in my next post, and look at the tabulation method that I use there. . .

Calculating cube roots in your head

I thought I would swing over to mathematics for a bit.

You don't need a real aptitude to enjoy maths, and even if you had woefully useless teachers (as I did),  you can still have fun with numbers.

Are you one of those people who play with numbers? I was, even was I was small, and when I was supposed to be sleeping, I would be lying in bed, going "2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 . . ." on and on, seeing how high I could go.

I usually got 22 or 23 terms before I lost track and had to start again. I just enjoy looking for patterns (or I fell asleep).

Sometimes, I find something useful, like a way to fool people into thinking that I had memorised the cubes of all the numbers from 100 to 200.

I developed this trick by looking at the final digit of various cubes:

If you cube a number ending in 1 the result ends in 1

If you cube a number ending in 2 the result ends in 8

If you cube a number ending in 3 the result ends in 7

If you cube a number ending in 4 the result ends in 4

If you cube a number ending in 5 the result ends in 5

If you cube a number ending in 6 the result ends in 6

If you cube a number ending in 7 the result ends in 3

If you cube a number ending in 8 the result ends in 2

If you cube a number ending in 9 the result ends in 9

and obviously,

If you cube a number ending in 0 the result ends in 0

See the pattern? If you know the last digit of the cube, you know the last digit of the seed number that was cubed.

Then I realised that you can memorise the approximate ranges for the cubes of 100 to 109, 110 to 119 and so on:

100 – 109 1 to 1.3 million

110 – 119 1.3 to 1.7 million

120 – 129 1.7 to 2.2 million

130 – 139 2.2 to 2.7 million

140 – 149 2.7 to 3.3 million

150 – 159 3.4 to 4 million

160 – 169 4.1 to 4.8 million

170 – 179 4.9 to 5.7 million

180 – 189 5.8 to 6.7 million

190 – 199 6.8 to 8 million

— so if I hear 1442897, I know from the first two digits that we are between 110 and 119, and the last digit of the cube (7) tells me the last digit of the number being cubed is 3, so the answer is 113.

Try it!