What if the rules had never been taught?

Something came up at my home site which might be of interest to the wider readership. It was a maths or math question:

Various readers gave answers, then my last answer [which I’d changed a few times] was this below, in comments.

[Warning – spoilers ahead if you’d like to try it yourself first]

Let’s do it again, Steely Dan.

Line 1

One boot is 5.

Line 2

Each unadorned boy is 5.

Line 3

The four cones make 8. One cone = 2.

All right, we have our values:

Boot = 5
Boy = 5
Cone = 2

In order to complete line four, we’re taught in school either BOMDAS or BODMAS. This is the sticking point for readers who may not have been taught this for complicated equations. From one of the many help sites:

Do you use Bodmas when there are no brackets?

Just follow the rules of BODMAS to get the correct answer. There are no brackets or orders so start with division and multiplication.



This is primary or elementary school, pretty much universal:


All right, in our example, there are no brackets to clear, and ‘of’ is just another name for ‘times’.

Does it matter if it is BODMAS or BOMDAS? I can’t answer – usually no I’d suspect. I learnt or learned BOMDAS.

As it’s irrelevant in our Line 4, pressing on, we solve the ‘times’ first. We know the adorned boy [from head down] is 5 for himself, 2 + 2 for the cones, plus 5 + 5 for the boots = 19.

BODMAS says:

19 x 2 = 38

Leaving us with:

5 + 38 = 43

All right, if we ignore the accepted method for exams and just go left to right instead:

5 + 5 = 10
10 x 2 = 20

But that does not stand up internationally:


My compounding error and I do apologise [apologize] was to assume all readers had been taught maths [math] at primary [elementary] till year eight. A thousand apologies.



The quote above mentions:

There are no brackets or orders

Now that’s interesting. I understood ‘O’ [letter, not zero] to stand for ‘of’, as in three-quarters of twelve.

But that seems to indicate it stands for ‘orders’, which actually makes sense, except that I was taught ‘of’.

‘Orders’ there I take as ‘special orders’ in post-year eight math[s]. And it makes sense.

[End spoilers]

Implications for us in the west

This is a political issue – rules of society – but even more to the immediate point – rules of computing, at least the rules underlying the rules.

Just what does happen when a generation is brought up without the old rules? That is – they were never taught these things?  They ‘missed out’?

Jaw drops open for someone like me.

17 comments for “What if the rules had never been taught?

  1. FrankH
    April 4, 2020 at 9:45 am

    The “O” in BODMAS (BOMDAS) is orders, which means exponents, e.g. squared, cubed, square root, cube root etc.

    Division and multiplication are just two ways of doing the same thing, as are addition and subtraction. E.g divide by 2 is the same as multiply by a half and 10 – 2 is the same as -2 + 10. So the DMAS part could be MDSA.

  2. John Tee
    April 4, 2020 at 10:06 am

    Line 1. Why are you assuming a plus sign between left shoes and right shoes?

    • FrankH
      April 4, 2020 at 10:34 am

      How many feet have you got? Why are you assuming a plus sign between your feet?

    • April 4, 2020 at 12:49 pm

      Default? Also last line seems to assume that.

  3. April 4, 2020 at 11:00 am

    Is any single shoe worth half of a pair of shoes?

    It depends whether one is dealing with a mathematical puzzle or real life.

    Real life says KISS (Keep it simple, Stupid).

    So in real life mathematical puzzles, a single shoe is worth half a pair.

    Best regards

    • April 4, 2020 at 12:50 pm

      Philosophy now. Like it.

  4. John Tee
    April 4, 2020 at 1:05 pm

    It is a poor maths question if the answer depends on interpretation. I think there is inconsistency here. On Line 1 you are all happy that the 30 on the right means thirty. Not 3 + 0 or 3 x 0. Yet on the left of the equation you are assuming (a) that a left shoe has the same value as a right shoe and (b) that they should be added together rather than treated in the same way as the digits on the right.

    On line 4, you assume that the value of a boy wearing shoes is a sum; but it could be a division, boy over shoes.

    On that basis I get:
    Line 1: 10 + 10 + 10 = 30. As you look at the pairs of shoes the one on the left (actually a right shoe!) is a ‘1’, the other is a zero.

    Line 2: 5 + 5 + 10 =20. Unadorned boy = 5.

    Line 3: 4 + 4 + 5 = 13. Pair of identical cones = 4, therefore one cone =2.

    Line 4: 1 + 5/10 x 2 = 1 + ½ x 2 = 1 + 1 = 2.

    The answer is 2.

    • April 4, 2020 at 3:20 pm

      We’re shirley assuming that it’s a Year 6 grade question. 🙂

  5. Lord T
    April 4, 2020 at 2:18 pm

    As they are pictograms we can’t assume that a graphic of a single shoe is the same as a pair. There is enough data there to work it out.

    We know pair of shoes are 10 by the first line.
    We know the creepy lout is 5 by the second line.
    We know the double cones are 4 by the third line
    There are two unknowns is the fourth line.

    We can assume about the shoes but the convention with 2Y is that it is 2 x Y when they are together so two boots together = Y x Z = 10. That could be 2 x 5 or 5 x 2 or another combination.

    • April 4, 2020 at 3:21 pm

      Not overthinking it?

      • Lord T
        April 6, 2020 at 10:35 am

        Of course. Not much else to do atm.

  6. Voice of Reason
    April 4, 2020 at 5:21 pm

    The general way of reading precedence is (MD)(AS), so that multiplication and division are the same level, so read left to right, as are addition and subtraction

    This is the general convention in Mathematics and programming languages, so

    1/2*x is (1/2)*x, not 1/(2*x)

    Why this so baffles people is beyond me.

    • April 4, 2020 at 5:41 pm

      Assuming the first means half of x and giving x an arbitrary, say, 6 value, then half of x is 3, whichever way it’s expressed. I’m assuming your using the asterisk as times, unless it has some other computer meaning.

      • Voice of Reason
        April 4, 2020 at 6:26 pm

        I am, as that is the standard symbol, to avoid confusion with ‘x’ as a variable.

        However, the people who insist that the MDAS is specifically an order of precendence would evaluate 1/2*6 as 1/12, not 3.

  7. Valentine Gray
    April 5, 2020 at 11:11 am

    We are essentially under Martial Law, and you are prioritising this tripe. I thought the Gove crap was bad enough.

  8. ph
    April 7, 2020 at 9:51 am

    All assuming Base 10…. different answer in Octal (base 8)

Comments are closed.