## 2020-06-17

### Logic puzzle?

Someone posted on a Facebook group this image, and said that "My pedantic 8 yo needs to know whether Sophie is included in the total."

Now, the answer is that is pedantic 8 yo does not actually need to know whether Sophie is included in the total or not in order to answer the question. i.e. whether Sohpie is a passenger or not.

Now, to me that is blindingly obvious. What puzzled me is not, for a change, trolls on the Internet, but that so many people (indeed, I think all but one) comment that she may be the bus driver and suggesting that matters. One person said to put the answer and "assuming Sophie was driving the bus". It seems almost everyone assumed that it mattered if she was a passenger or not, and hence if she was included in the total.

I would to normally do this, but I'll explain the incredibly simple logic just to be clear to anyone that is in some doubt somehow.

• If she is a passenger, there are 17 passengers INCLUDING Sophie, and 21 are added making 38 total passengers including Sophie, as she is a passenger.
• If she is not a passenger, there are 17 passengers NOT INCLUDING Sohpie, and 21 are added making 38 (plus Sophie who is not a passenger).

Either way the answer is 38.

Of course, what the pedantic 8 yo should have asked (and kudos for asking questions at all), is are all the "people" that got on "passengers". After all, if they are, then why not say "21 more passengers get on"? Why use a different word ("people") in that part of the question.

Yes, if Sophie is one of the 21, and not a passenger (e.g driver), then just like any other case where the 21 are not all passengers, it changes the answer - but that because the 21 are not all passengers rather than Sophie's status as such.

1. Carrying on the pedantry, Sophie may not be anywhere near the bus at all but could be the owner of it. Still doesn't make a difference to the number but adds a third scenario. She's neither the passenger or the driver

2. 17 passengers but no driver are on board. 21 people then get on, made up of 20 more passengers and one driver. The bus now departs with 37 passengers!

Sophie could own the bus. Sophie could be the delayed driver for the bus, one of the 21. I don't think Sophie matters here, it's the passengers vs people bit that the pedant needs to focus on.

3. I wonder if it would actually be incorrect to say "21 more passengers get on the bus", because in order to be a passenger, you actually have to be ON the bus, not waiting to board it. At the time when they are getting on the bus, they are just people, or maybe "intended passengers", rather than actual passengers.

So to be pedantic, we would have to say "21 more people get on the bus and become passengers", which also resolves the ambiguity over whether any of those 21 people are actually drivers, conductors, tea servers or anything else.

4. I guess the main question is.... Is there any reasonable interpretation of the question that could give an answer other than 38? I haven't seen one yet. The closest us Nick Burch's suggestion that the 21 could include the driver, but I would argue that the use of the phrase "more people" suggests that in this question, 'people' and 'passengers' are synonyms and therefore the driver is not involved in the calculation at all.

On the subject of getting wound up about test questions - my son was doing a practice GCSE physics paper yesterday. The question was about an electronics circuit. The diagram showed the positive end of a 9v power supply connected to a 100K resistor which connected to an unmarked thermistor which connected to an ammeter which then connected to the negative terminal of the power supply. A voltmeter was connected in parallel with the thermistor. The question read "What quantity is measured by the ammeter?".

1. I think you're overthinking your son's physics question. The answer is "current".

They aren't asking you to calculate a value (for which you'd need the resistance of the thermistor).

2. Agree but. Q should be "What is measured by an ammeter?". Whole Q designed to confuse and diagram unnecessary. Is current a quantity? Amps is a quantity.

5. The question says nothing about the number of people who might get _off_ the bus.

6. The 8 year old's question is fairly reasonable. "Sophie's bus" is reasonably interpreted as "the bus that Sophie drives". If ownership, it would be "Stagecoach's bus" or whatever company has done its sweet deal with the local council - individuals don't generally run passenger routes. If Sophie is a passenger, her naming is redundant, and the question might as well have said "a bus". This interpretation follows Polya's _How to Solve It_, which advises us to make sure we've used all the information in a given problem.

If Sophie is included in "the total", being the sum 17 + 21, then there are 37 passengers and 1 driver on the bus. If Sophie is not included in the total, she EITHER hasn't got on yet OR is disregarded, and there are 38 passengers on the bus - the point being that Sophie is potentially part of the additional 21, but not the initial 17.

Now you could say, "Oh but what if >1 of those additional 21 aren't passengers". But, excepting exceptional circumstances, people become passengers upon mounting a bus that's already full of passengers, unless they're the driver who has just returned from having a tea or a wee or a fag. If we're gonna worry about edge cases like those who are jumping on and off stationary buses for giggles, we can worry about people who give birth upon entry, who die upon entry, and so on.

This all said, "more" suggests people not mentioned before, so Sophie is /unlikely/ to be part of the additional 21. But the 8-year-old has still asked for what is practically speaking likely to be the most relevant piece of information in determining the answer. Which, for applied mathematics, is a great skill that adults often lack, let alone 8 year olds.

1. If Sophie is included in the total she is, by definition, a passenger and so in the 17 or 21. The answer is always 38 whether she is a passenger or not. The only assumption is the 21 are all boarding as passengers, so whether sophie is one or not is not relevant to the answer, which is 38 either way.

2. Tom I think you're missing the key point.

The question does not say "Sophie's bus has 17 PEOPLE". It says "Sophie's bus has 17 PASSENGERS". So whether or not Sophie is counted among those passengers is irrelevant; either way we know there are 17 of them because it says so right there in the question.

Since our task is to count the passengers, the only ambiguity is about whether or not all of the subsequent 21 people who get on are also passengers and should be counted. It seems clear that the use of people in the second sentence is just stylistic (to avoid repeating the word passengers) and so the answer is plainly 38.

Whether Sophie is one of the 38 or not has no effect whatsoever on the answer.

3. Another way of looking at it is that since there is no information about who Sophie is or what function she performs (if any) in relation to the bus, or even whether she is actually ON the bus or just a remote owner of a bus company, we can completely disregard her existence and act as if no names were mentioned in the question at all. In other words, the fact that this fictional world contains a fictional person called Sophie provides no informational content relevant to the question.

"A bus has 17 passengers. 21 more people get on. How many passengers are on the bus now?"

Nobody at this point would respond "It depends if one of the original 17 passengers is the driver", because the question specifically calls them "passengers" and the driver is not a passenger. The only possible room for pedantry is the question of whether all of the 21 additional "people" are also passengers.

7. I think I've figured out a way to not have 38 passengers at the end, but only if we're allowed to assume additional actions not mentioned:

1) 17 passengers on the bus, plus Sophie is the driver
2) 21 people get on the bus, consisting of 20 new passengers, and 1 new driver
3) Sophie departs the bus (and likely drives off in the car the new driver arrived in)
4) We now have 37 passengers on board, plus the new driver

8. Ah, or an even simpler option:

1) 17 passengers on the bus. Sophie may or may not be a passenger, it really doesn't matter here
2) 21 people get on the bus, consisting 20 passengers and 1 ticket inspector
3) We now have 37 passengers, 1 driver, and 1 ticket inspector

9. In this day and age it may well be that of those 21 people getting on 10 are revenue protection officers and hence not passengers but staff checking that all of the passengers have valid tickets. I go with the poor wording suggestion. It should be "21 people board the bus and become additional passengers."

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