# Challenge Riddles and Puzzles: Extend the following to a valid equation

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#### mfb

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I give up. I wonder if the answer may lie outside my realm of experience.
Forget numbers. Count circles.
f(0)=1, f(1)=0, ..., f(8)=2.

#### fresh_42

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2018 Award
Forget numbers. Count [topological] circles.
f(0)=1, f(1)=0, ..., f(8)=2.

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Forget numbers. Count circles.
f(0)=1, f(1)=0, ..., f(8)=2.
It's no wonder it eluded me=I don't feel so bad. It's quite clever, but somewhat un-mathematical.

#### fresh_42

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2018 Award
It's no wonder it eluded me=I don't feel so bad. It's quite clever, but somewhat un-mathematical.
No it is not, just unconventional. It counts the genuses of concatenated topological geometric objects. On the left we have words of a formal language without grammar, and every letter has a weight. I wonder if we could make a baric algebra out of it.

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#### fbs7

Got it after the preschool hint.
Holly Choo-Choo!!! You are a genius!!!

#### Orodruin

Staff Emeritus
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Since @mfb has solved number 3, here comes the next one:

4. In one of three urns there are two white balls, in another a white and a black ball, and in the third two black balls. The urns are labeled: one sign says WW, one WB and the third BB. But someone has switched the signs so that none of them specify the contents of the individual urns anymore.

One may take a ball from one of the urns, one after the other (without looking into the urn) until it is clear which urns contain which of the three ball pairs. How many balls do you have to take out at least to reach this goal?
One ball.

Let small letters denote true content and capital letters labelled content.

The urn WB is not wb, so it must be bb or ww. Taking a ball out of it will therefore tell you which it is. If we get white out of WB, then it is ww. We are now left with the urns WW and BB. We know that those labels are wrong and that one of those urns is bb != BB. Therefore bb = WW and wb = BB. The corresponding argument goes if we get black out of WB, but exchanging the roles of the blacks and whites.

This can also be seen as follows: There are two possibilities for labels:
{WW = wb, WB = bb, BB = ww} or {WW = bb, WB = ww, BB = wb}
Clearly they cannot be discriminated without taking a ball out. If we take a ball out of WB, it will distinguish between the two possible cases.

#### fresh_42

Mentor
2018 Award
5. Let's have some fun. We will perform a 4 step manager test. I will post 4 questions step by step, i.e. question 2 if the first will be answered correctly etc. It is an old joke, but here I will add a "lessons learnt" comment after each question.

a. How do you get a giraffe into a fridge?

#### mfb

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Open the fridge, put the giraffe in, close the fridge.

#### fresh_42

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2018 Award
Open the fridge, put the giraffe in, close the fridge.
This question investigated whether you tend to find much too complicated solutions of very easy problems.

5.b. How do you get an elephant into the fridge? (@mfb please pause on this one.)

#### jbriggs444

Homework Helper
This question investigated whether you tend to find much too complicated solutions of very easy problems.

5.b. How do you get an elephant into the fridge? (@mfb please pause on this one.)
Open the fridge, take the giraffe out, put the elephant in, close the fridge.

[Zoning into the apparently expected level of abstraction]

#### fresh_42

Mentor
2018 Award
Open the fridge, take the giraffe out, put the elephant in, close the fridge.
This question investigated whether you are aware of the consequences of your doings.

5.c. The Lion King is holding up his yearly conference of all animals. However, one is missing. Which one?

#### Orodruin

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5.c. The Lion King is holding up his yearly conference of all animals. However, one is missing. Which one?
The elephant. He is in the fridge.

#### fresh_42

Mentor
2018 Award
The elephant. He is in the fridge.

5.d. You have to cross a river where dozens of crocodiles live. How do you resolve this situation?
(@Orodruin to pause).

#### jbriggs444

Homework Helper

5.d. You have to cross a river where dozens of crocodiles live. How do you resolve this situation?
(@Orodruin to pause).
Oooh oooh, can I go again?

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Homework Helper

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2018 Award

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#### jbriggs444

Homework Helper
Oh silly me. The crocs are at the annual get together.

#### fresh_42

Mentor
2018 Award
Oh silly me. The crocs are at the annual get together.
Yes, you swim.

This question was about whether and how fast you learn from mistakes. (Although we had none.)

According to a study by Andersen Consulting, around 90% of all tested executives worldwide have answered all questions incorrectly.

Andersen claims that this clearly disproves the thesis that executives have the mental faculties of a four-year-old.

#### fresh_42

Mentor
2018 Award
6. How many years of life did somebody complete on the first day of the year 30 AD, if he was born on the last day of the year 20 BC?

#### mfb

Mentor
More of a history question - there was no year 0. The last day of 1 BC he was 19 years old, the next day was the first day of 1 AD. The last day of 1 AD he was 20 years old, the last day of 29 AD he was 49 years old -> 49.

You find a historic letter dated 5 BC talking about an event that happened 20 BC. What is wrong?

#### fresh_42

Mentor
2018 Award
More of a history question - there was no year 0. The last day of 1 BC he was 19 years old, the next day was the first day of 1 AD. The last day of 1 AD he was 20 years old, the last day of 29 AD he was 49 years old -> 49.
Correct analysis, wrong count.
You find a historic letter dated 5 BC talking about an event that happened 20 BC. What is wrong?
The five is wrong. The description of the twenty is not specific enough to be wrong, since it could also mean fifteen years prior to the letter, i.e. relates the dating to the impossible gauge.

#### mfb

Mentor
Correct analysis, wrong count.
Oops, 48 of course. 20+28 is 48, not 49.
The five is wrong.
Right. You can make the same puzzle with a letter e.g. 20 AD, but then you need to figure out when the AD counting was introduced (long after that), so the puzzle is easier with BC.

#### lpetrich

You find a historic letter dated 5 BC talking about an event that happened 20 BC. What is wrong?
That dating system did not exist at the time, so that document could not have referred to such dates. So such dates would be a present-day interpretation of whatever dates that it used.

"Riddles and Puzzles: Extend the following to a valid equation"

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