I was drive home today and was pondering about dozenal base 12, which I haven't done for quite some time, and it made me want to have a website/newsletter with a daily question.

Does anyone know of a website that has this? Or something like it?

The reason I would like this is because it would give me a reason to think about dozenal math each day. And if I start to think about it regularly and actually do a little practice daily, well then it will become more natural.

I like the idea of moving to a base 12 number system, but without actually using it then I just forget about it. And I haven't been the activist to go out of my way to really make myself problems with it. So even just some basic addition or multiplication question each day to keep reminding me about base 12 would be cool. Heck, I could really go for one of those page a day calenders with a dozenal equation for each day.

Just thought I would share my thought.

EDIT: I guess I could have thrown this into the number bases forum. If a mod feels it fits there better then feel free to move it.

We can certainly post problems for you to try. The DSA used to have an Aspirants Test that might do.
I can post a problem a day if you like.
For starters, maybe you'd like to try this set (adapted to dozenal from an old maths book); all working to be done in dozenal:

Well, that is exactly the kind of thing I was hoping to find. Gives me an extra reason to come to the forum each day too. This will definitely help me if it is something your willing to go through the work to do. Hopefully others will also be interested in doing some daily dozenal math. Optimistically something like this may help out the community, either way it helps me out.

Perhaps the solutions could be posted the following day with the next question?

Many Thanks Shaun :lol:

These are easy.

#1: 4
#2: 9'6"
#3: 3"
#4: 3'
#5: 6'
#6: 13'6"
#7: 6"
#8: 8 shillings
#9a: 2'6"
#9b: 3
#:A: 11'6"
#:B: 1'6"
#10: 11'6"
#11: 15"

But I don't think we'd use the ' and " notation for feet and inches when we could just write inches as a dozenal fraction of feet.

True.
This page was adapted from a real aritmetic book page by altering the numerals and leaving the text as it was.

OK something different - taken from the Miscellaneous Examples of a nineteen-fifties arithmetic.

(289/447)
A Portuguese barrel contains *24'3 English gallons. If a French cask contains *49'14 gallons, find the smallest whole number of gallons which will fill an exact number of Portuguese barrels, and which will also fill an exact number of French casks. (The original question used fractions.)

(6/430)
The area of Scotland is *152TE square miles and the average number of inhabitants to each square mile is *124. Find the whole population.

And here's one I like - a (pre-decimal) penny weighs a third of an ounce. How much is a ton of pennies worth? (NB "long ton" of *1368 lbs, not the US "short ton" of two thousand.)
(Answer in any suitable dozenal units.)

Will these do - or do you want something less wordy?
S

Dan - your answers aren't showing up in Firefox.

NB: Question 8, 16 ft @ 6d /ft
The 16 is in dozenal too, so the answer is *16 x 0'6 shillings, or 9s.

Spoiler prevention. Highlight them.

These are just fine. Wordy is often quite practical.

I have a caution though. I've gone through school with nothing but metric, and I'm completely unfamiliar with imperial units. I doubt this will be any problem if I just treat them as straight units, and if I have questions on the units I can look them up on wikipedia. But for an example with question 8, I had no idea it had to do with shillings.

I hadn't thought of that. Took it for granted that everyone knew a shilling (s) was twelve pence (d) ...

Answers:
*34 gallons to *68 barrels
*102 gallons to *E4 casks

*52280d or *5228s (or *£314)

Population: 1,871,858

Miscellaneous exam questions (p481) adapted to dozenals.

(123)
In the Soudan 1 rotl is equal to *100 dirhens and 1 oke is equal to *294 dirhens.
If 1 oke is approximately 2'9 lbs find the number of ounces in 1 rotl (to 1 dozenal place). (1 lb = *14oz)

(124)
If £1 is equivalent to 17'04 pesos and one dollar is equivalent to £0'248,
find the value of ten dollars in pesos correct to two places of dozenals.


(125)
A man changed 144'60 marks into francs, obtaining E'78 francs to the mark.
He then spent 135E francs and changed the remainder into English money at the rate of 8 francs to the shilling.
Find, correct to the nearest shilling, how much English money he received.

(If the exchange-rates look strange, remember the examples were set in the fifties.)

Canada has become the land of all metric, and it is quite rare to hear about old European units of anything. Or so I've found. But I've also found my rock to be quite comfortable to live under.

Here's my question for today:

A wide variety of computer programs, from games to cryptography, rely on sequences of random numbers. Although it's possible to get "true" random numbers with hardware that measures electrical noise, most applications use "pseudo-random number generators" that produce sequences that look random but are actually mathematically determined by previous numbers in the sequence.

One of the earliest PRNGs was the middle-square method. To generate "random" 6-digit numbers, you square the previous number, producing a 12-digit number, and take the middle 6 digits. Equivalently,

f(n) = (f(n-1)² div 1000) mod 1000000

For example, starting with the "seed" f(0) = 123456, you get the sequence

f(1) = 241383 (= middle 6 digits of 123456² = 15241383936)
f(2) = 265752 (= middle 6 digits of 241383² = 58265752689)
f(3) = 624125
f(4) = 532015
f(5) = 39960
f(6) = 596801
f(7) = 171433
f(8) = 389273
f(9) = 533468
f(10) = 588107
f(11) = 869843
f(12) = 626844
...
f(144) = 352881
f(145) = 525000
f(146) = 625000
f(147) = 625000

After this, the generator will just keep giving 625000 forever. In general, once one of the numbers 0, 1000, 376000, 495475, 625000, or 971582 occurs, the middle-square method gets stuck. This fatal flaw led to the disuse of the method.

Changing to dozenal would not improve matters, because there are 8 numbers the middle-square method could get stuck at (i.e., numbers N such that (N² div *1000) mod *1000000) = N. What are they?

No-one's asked for the answers ...
But here they are:

(123) 13'T ounces
(124) 31'T7 pesos
(125) 7 shillings

Any more wanted?
Like these?
Something different?

Keep them coming. I like these kind of questions, but I would also like some fairly basic questions like the first example. I've honestly had some difficulty with a few questions, but it gives me something to work at (and is also a bit of a reminder for some basic math stuff too).

So in my opinion:
-Word problems are good. Helps me to translate real problems I encounter in the world to math.
-I would like some simple questions to practice basic skills. Elementary calculations like (13.5x2.8)-14.9. Kinda like what it was for the first question.
-I also like a couple questions like the word ones you had that involve least common multiple, etc. Which for me is actually challenging in dozenal. Probably just because I haven't done it much.

I haven't been online as much, and won't be for the next couple weeks, because I'm in the middle of a big move.

So thanks for the questions guys! I will likely do everything you put up even if I'm not around as much the next couple days. I also liked your question Dan, thanks
:lol:

Here's some questions taken from the exit-level TAKS test:

(All numbers dozenal)

• A basketball player made 10 free throws in his last 30 attempts. How many free throws would the basketball player be expected to make in 66 attempts?
• The drama department at McHenry High School has built a stage floor in the shape of a regular octagon. The length of each side of the octagon is 4 yards. What is the approximate area of the stage floor?
• If XY=8 feet and XY=15 feet, what is the area of triangle XYZ? [Diagram shows a right angle at point Y.]
• What is the approximate distance between the points (-7, 2) and (Ɛ, -5)?
• A large cheese pizza at Palanzio’s Pizzeria costs $6.Χ plus $0.Ɛ for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.4 plus $0.8 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza in order for the pizzas to cost the same, not including tax?
• If (5.4, y) is a solution to the equation 5x − 4y − 18 = 0, what is the value of y?
• Karen, Simone, and Cameron contributed $54 altogether to pay their phone bill. Karen’s contribution was four dollars more than twice as much as Cameron’s. Karen’s contribution was three times as much as Simone’s. What situation? was the amount of Cameron’s contribution?
• Mr. Jenkins designed a true-false science exam. The ratio of true answers to false answers is 5:3. What is the pergrossage of true answers on Mr. Jenkins’s science exam?
• In 11ΧΧ, people in Laredo, Texas, erected the tallest flagpole in the United States. It can be seen from miles away. [Diagram: A mirror lies flat on the ground 186 ft from the base of the flagpole. A 6.3 ft tall man is standing 5 ft further back and sees the top of the flagpole in the mirror.] According to the information shown in the drawing, what is the approximate height of the flagpole?
• A salesman at a jewelry store earns a salary of $207 per week plus a commission of 1Χ per gross of his weekly sales. If the salesman earned $660.4 in a week, what was the amount of his sales for the week?
• Look at the diagram below. [Diagram: Door with a handle 5.6 inches long.] When the door handle is pushed down to open the door, it makes a 39° angle with its former position. What is the approximate arc length of the path traveled by the outside end of the door handle when the handle is pushed down?
• If the perimeter of the equilateral triangle shown below is 31 centimeters, what is the approximate area of the triangle? [Diagram: Pointless]
• On a certain math problem, Cynthia mistakenly divided a number by 4 and then subtracted 20 and got 10 for her answer. After reading the problem again, she realized that she should have subtracted 20 before dividing by 4. What was the correct answer?