Category Archives: Venn diagrams

Logic puzzles – about old jacks and new coats

Here are some new puzzles:
1) Old jacks
(1) Leather jacks always become very old
(2) Old jacks turn brown
Which conclusion is valid?
a) All brown jacks are old
b) No old jack is blue
c) Some leather jacks are brown
d) None of the above
You can check your answer at solution 85

2) Dirty Pigs
(1) No dirty pig is fat;
(2) No meager pig is pink;
Which conclusion is valid?
a) All fat pigs are clean;
b) All dirty pigs are meager;
c) All pink pigs are fat;
d) All pink pigs are clean;
e) All of the above;
You can check your answer at solution 96

3) New coats
(1) No new coat of mine is not made of plastic;
(2) All plastic coats are closed with zips;
Which conclusions are valid?
a) All plastic coats are mine;
b) All zipped coats are mine;
c) All coats closed with zips are old;
d) All my new coats are closed with zips;
You can check your answer at solution 75

These puzzles are based on a mathematical concept called Sets, but you can solve them without this knowledge. Sets are now taught at all high schools in the Netherlands, and I suppose also in other countries. Some Googling on Venn diagrams and puzzles revealed little or no sites. This surprises me as it usually regarded as a good educational practice if students are also taught to apply their knowledge to practical problems, although this may depend on the preferred learning style of the student.

Puzzles of this type do have a history. One not so well know puzzle master from Victorian England is Charles Lutwidge Dodgson (1832 – 1898), better known as Lewis Carroll, author of children tales as Alice in Wonderland and Through the looking glass.

In his daily life he taught mathematics, and the story goes that Queen Victoria loved Alice in Wonderland so much that she wrote the author and asked for a copy of his next book. Charles felt honoured, and duly send her a copy of his next book – a treatise on a mathematical subject.

Charles was also an avid puzzle designer. In his books “Symbolic logic” and “The game of Logic”, later republished by Dover press, he devised an elaborate mechanism to solve set problems like those above. Modern mathematicians would use Venn diagrams to solve the same class of problems. Puzzles like these are somtimes called Soriteses.

Here are some examples of the type of puzzles you can find in his book:
4) Wasps
(1) All wasps are unfriendly
(2) All unfriendly creatures are unwelcome
What conclusion can be found?

The puzzles can be made slightly more complex by adding mote statements, by more types of objects that play a role, or by adding negatives. Here are some of his puzzles that comprise 3 statements:
5) Sane
(1) Everyone who is sane can do Logic
(2) No lunatics are fit to serve on a jury
(3) None of your sons can do Logic
What conclusion can be found?

6) Flowers
(1) Coloured flowers are always scented
(2) I dislike flowers that are not grown in the open air
(3) No flowers grown in the open air are colourless.
What conclusion can be found?

7) Showy talkers
(1) Showy talkers think too much of themselves;
(2) No really well informed people are bad company;
(3) People who think too much of themselves are not good company.
What conclusion can be found?
Lewis Carroll was thinking in terms of modern day sets, and made no secret of it. At the end of each puzzle, he added a note about what the Universe of discourse in that puzzle was, wand what sets needed to be considered. For example, in puzzle 4 this was:
Universe = persons; a=good company; b=really well-informed; c=show talkers; d=thinking too much of ones self;

It is of course possible to create puzzles in this vein with more statements. Here is one from Charles L. Dodgsons book with four statements:
8) Birds in the aviary
(1) No birds, except ostriches, are 9 feet high;
(2) There are no birds in this aviary that belong to any one but me;
(3) No ostrich lives on mince pies;
(4) I have no birds less than 9 feet high;
What conclusion can be found?

Dodgson constructed puzzles much more complex; his longest is made up of 10 statements:
9) Animals in the house
(1) The only animals in this house are cats;
(2) Every animal is suitable for a cat, that loves to gaze at the moon;
(3) When I detest an animal, I avoid it;
(4) No animals are carnivorous, unless they prowl at night;
(5) No cat fails to kill mice;
(6) No animals ever take to me, except what are in this house;
(7) Kangaroos are not suitable for pets;
(8) None but carnivora kill mice;
(9) I detest animals that do not take to me;
10) Animals, that prowl at night, always love to gaze at the moon.
What conclusion can be found?

Odd one out


A while ago I suggested an “odd one out” at the gbrainy group discussion, and was quickly reproached for overlooking a hasty made up example. No excuse of course, and the other was completely right.
While surfing around this week I encountered another odd one out at Tanyas blog, see the illustration above. No solution given this time, and rightfully so. You are welcome to comment your solution 🙂

As an illustration of the dangers of odd one out, I just did a bit of surfing, and found this one as part of an established IQ-test:
Ο pen
Ο paper
Ο pencil
Ο crayon
The answer given was “paper”, as paper is the medium on which we write or draw, while crayon, pen and pencil are devices with which we write or draw.
The answer could as well have been Crayon, because it is not an everyday object, or because it starts with a ‘p’.

Despite these apparent dangers, there are some nice puzzles to be created in this category, and I hope to get back to this topic in a later post.