I have posted a small series of truth or lie puzzles at this blog, you can find them here.

This week I have just a link for you. Russian born USA mathematician published a nice puzzle here. It’s a toughy.

**Rikudo**^{**/*****} essentially are made up of a (partially hidden) string of the numbers 1 to N embedded in a figure consisting of hexagons.

I must admit I never figured out how to efficiently draw a couple of hexagons, so I’ll use squares arranged alternating in adjacent rows – the net result is identical in terms of the number of adjacent borders.

Usually, the number 1 and the highest number are given. Sometimes the author puts a dot on a border to indicate that the adjacent numbers differ by 1.

**Solving strategies**

A straight line between two given numbers, with the length of the line equal to the difference between the two numbers

Two adjacent hexagons have numbers which differ by two

No dead ends

Though there are several routes from 6 to 10, only 1 will fill the red square.

You can check your solution here

There are many, many puzzles about clocks and time. In the nineteenth century, both Henry Dudeney and Sam Loydd designed a number of them, and in a future post I may collect them.

**1) Basics**^{*/*****}

Today I encountered this problem on twitter, posed by a teacher for his students in primary school. Whisper your solution in the ear of the teacher to enter the classroom.

You can check your solution here

New puzzles are published at least twice a month on Fridays.

Pluszle® is the trademarked name of a new type of number puzzle I encountered in the book/magazine shop at The Hague CS. I didnt want to buy it, but today my wife bought me a copy. The rules for the puzzle are elegantly simple. The grid is filled with numbers, and you have to cross out numbers till the sum of the remaining numbers equals the numbers in the right and bottom margins.

Priced at 4,95 euro and containing 375 puzzles it doesn’t sound like a bad deal. The main problem seems to me that the first part of the booklet contains 3×3 and 4×4 puzzles. In my humble opinion, these could have been omitted. Just this morning I was tweeting about education, automation of arithmetic, and differentiation in exercises for different students. Maybe I would have loved it to get puzzles like these at primary school as extra exercises.

The booklet is produced by Pluszle BV in Leusden, and outsider in the Dutch puzzle magazine world, which is dominated by Denksport and Sanders puzzels. Their website at http://www.pluszle.com mentions apps for the I-store and the android store, but I must admit I didn’t try the app.

Another, albeit smaller problem, is that the main variation is the size of the grids: the larger the more complex. It isn’t too difficult to create similar problems with multiplication:

4) 5×5 nr3^{*/*****}

Another variation I can think of is a 4×4 grid with subtraction: cross out two numbers in every row and column so that the difference is the number in the right or bottom margin.

There is an even more puzzling form, but I think I reserve that for a subsequent post.

Now my words above may sound like a negative judgment, but I do not intend them to be that way. The larger sizes 6×6 and above, do offer a fair agree of difficulty.

**Solution strategies**

There are several solution strategies, here are the main ones:

(a) 8 can not be there, >5

(b) 3 can not be there, not in any combi

(c) 6 must be there, else you can not add up to 15

(d) all numbers must be there

When I got geography at primary school the main things I remember is that I had to learn which provinces we had in the Netherlands, and which towns are located where. At secondary school, the scope was broadened to Europe, the rest of the world. Of course, the location of major mountain ranges and rivers was included, again the form of “What is the name of this mountain range?” or “Where is river X?”.

This weeks puzzle is not so much a puzzle as an alternative geography test. If you are a geography buff, try your hand at this! The first question is a traditional question, to get you going, but the remaining questions require you to work with your geography knowledge in an unconventional way.

(Nearly) Everybody knows a lot more about the area close by than about countries far away. For this reason this questionnaire differentiates between USA, Dutch/European, and other countries. For these last, I welcome additions in the remarks section at the bottom of this post.

Rule: answer from your head – do not consult an atlas or wikipedia.

USA

===

1) What is the capital of the State Arkansas?

2) Which states border the state of Missouri?

3) Mention three state capitals that start with the letter “D”.

4) Through which states does the river Rio Grande flow?

5) Which state has a larger surface: Wisconsin or Wyoming?

6) What is the largest (in terms of population) city in the state Alabama?

7) Which primary interstate highway serves the most states?

8) Geographical knowledge should also encompass knowledge not directly related to your home country. Which countries does Bolivia border in the west?

Europe

======

1) What is the capital of Ukraine?

2) With which countries does Austria share a border?

3) Mention 3 capitals starting with a B?

4) Through which countries does the river Donau flow?

5) Which country has a greater area, Austria or Czech republic?

6) Which capital has more inhabitants, Berlin, Londin or Paris?

7) Mention 5 countries in Europe with mountains above 3000 meters.

Asia

====

1) What is the capital of Cambodia?

2) With which countries does Afghanistan share a border?

3) Mention 3 capitals starting with a “D”

4) Through which countries does the Mekong river flow?

5) Which country has a greater area, Thailand or Iraq?

6) Which capital has more inhabitants: Manila or Riyadh?

7) What is the length of the longest highway in China?

Netherlands

==========================

1) What is the capital of Noord Holland

2) Which provinces border Gelderland?

3) Noem 3 steden met meer dan 100.000 inwoners die met de letter D beginnen

4) Door of langs welke provincies stroomt de rivier de Maas?

5) Welke provincie heeft een groter oppervlak: Drenthe of Limburg?

6) Welke stad in Gelderland heeft de meeste inwoners?

7) Door welke provincies loopt de A4?

You can check your solution here

New puzzles are published at least twice a month on Fridays.

Last week I purchased another snake. It is not the first one I obtained, and if its price wasn’t ridiculously low at 4 euro, it would have remained in the shop at The Hague (or was it Utrecht?) Central station. The producer is listed as Clown Games.

You can read about the previous one here.

The packaging consisted of plastic, which I had to cup open.

At 4 euro it was so cheap that wondered if it would fall apart before i finished the booklet with examples, but it actually turned out to be sturdy, and even to a degree where it requires some force to turn.

The little instruction leaflet contained just 4 figures:

These can indeed be constructed:

There are numerous figures one can make with the snake. Credits for the following figures mostly go to my wife Jos and our daughter Margreet:

Have a look at at this diamond – it is made up of 10 triangles.

Your challenges are:

**1) 8 triangles**^{**/*****}

Move 4 matchsticks and have 8 triangles

**2) 7 triangles**^{**/*****}

Move 4 matchsticks and have 7 triangles

**3) 6 triangles**^{**/*****}

Move 4 matchsticks and have 6 triangles

**4) 5 triangles**^{**/*****}

Move 4 matchsticks and have 5 triangles

You can check your solution here

New puzzles are published at least twice a month on Fridays.

In the past I published several posts on river crossing puzzles. I think together they are the most extensive resource on river crossing puzzles on the web.

I used the week between Christmas and New Year to look for apps. To my surprise, there was just one, and it held just a few puzzles. Well, it did in spire me to:

**1) The Autists and the Lazy.**

Six people want to cross a river. They have a boat which can hold only 2 people at a time.

* Two of the six people are autists. They don’t want to be in the boat with any one else, though they don’t mind being on the same shore.

* Two of the people are outright lazy, and don’t want to row.

* The remaining two people are normal.

How many crossings does the boat have to make?

You can find the old posts here:

* Man, wife and kids – river crossing 1

* The farmer, the wolf, the goat and the cabbage – 2

* Three couples – river crossing – 3

* Bigamists – river crossing – 4

New brainteasers are published twice a month on Fridays.

You can check your solution here

This week we have an honoured guest – Alice. Yes, Alice from Alice in Wonderland!

Alice heard Tweedledum say: Yesterday we got a number of wine gums. We both got the same number, but we played a game which I won and then I had 5 times as many wine gums as Tweedledee. But when I gave him one of my wine gums, I had only 4 times as many wine gums as he had.

This week we have an honoured guest – Alice. Yes, Alice from Alice in Wonderland!

Alice heard Tweedledum say: Yesterday we got a number of wine gums. We both got the same number, but we played a game which I won and then I had 5 times as many wine gums as Tweedledee. But when I gave him one of my wine gums, I had only 4 times as many wine gums as he had.

1) How many wine gums did Tweedledee and Tweedledum have?

That’s strange, Alice said. Yesterday, I mean the day before I fell into this rabbit hole, I had been playing a game with my sister. We were playing for matches, and after the game I had 7 times as many matches as my sister. But when I gave her one of my matchsticks, I had only 6 times as many matches.

2) How many matches did Alice and her sister have?

I was telling the story above to a little girl called Alais. Alais thought for a moment, then told me: That is strange. Yesterday, the day before you told me this puzzle, I was playing a game with my little sister. After the game, I had 10 times as many gumdrops as she had. Of course I gave her one, and then I had exactly 9 times as many as she had.

3) Alais is obviously a very smart girl. I knew she had had some elementary algebra at school. She had obviously figured out that there are an infinite number of numbers with which this puzzle can be told. Can you explain why?

You can check your solution here

New puzzles are published at least twice a month on Fridays. Solutions are usually published after one or more weeks.