4 squares

This puzzle was inspired by a puzzle in one of the many Mensa puzzle books, “”Logic brainteasers”, by Philip Carver and Ken Russell.

You can check your solution here

Geometry – or is it?

1) Three squares^**/*****



On twitter I found the account of a very kind and smart lady called Catriona Shearer, who poses a lot of very nice and original math problems. One problem is reproduced here with her permission. In the figure above, the sides of the three squares are three consecutive integers. The length of the black line is 4√10.
What’s the total area?

You can check your solution here

2) Four squares^***/*****
The puzzle above inspired me to the following puzzle:

The length of the sides of the three smaller squares are all natural numbers – integers if you prefer that term. The length of the side of the big square is 6√10.
What is the size of the three small rectangles?

New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

You can check your solution here

Add a nine to the end of the number

1) Adding a nine^***/*****
2² = 4. Writing a 9 after it, I get 49 which is 7²
4² = 16. Writing a 9 after it, I get 169 which is 13²
What is the next square number, which, when adding a 9 after the number, is a square?

You can check your solution here

New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Resolf

Resolf puzzles consist of four triangles, with three numbers at the corners of each triangle and the sum of the three numbers in the center.

I first encountered them in a publication by Sanders Puzzles.

An example of a solved resolf looks like this:

Nr 1^*/*****
Use the numbers listed below the triangle to make the sums

Sanders puzzles regularly also uses multiplcation:
Nr 2^**/*****

And one can extend this machanism to all 40 basic arithmetic operations:
Nr 3^***/*****

You can check your solution here

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

Rikudo

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

1. 
   A straight line between two given numbers, with the length of the line equal to the difference between the two numbers
   
   


2. 
   Two adjacent hexagons have numbers which differ by two
   
   


3. 
   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

Clocks and time

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.

2) Advanced^***/*****

You can check your solution here

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

Pluszle

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.

1) 5×5 nr 1^*/*****

2) 5×5 nr 2^**/*****

3) 6×6 nr 2^**/*****

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

Plastic snake

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:

Alice and the sweets

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.

It’s just chance – or is it?

Searching for puzzle apps on my android phone, I encountered “Probability puzzles” by “atorch”. Nice puzzles, although this type of puzzle never was one of my favorites and probably never will be. The app is working well, and the puzzles are varied. Well recommended.

Probability actually has its root in betting and games of chance. I was reminded of this when I was downloading the “Print and play” game Fazenda. Unfortunately the dice were missing.
In the rules of Fazenda, there are three dice. All 18 sides are either brown or blue.

Three dice^**/*****
This weeks problem is this
Suppose that the three dice are identical, and that they each have 2 brown and 4 blue sides, what is the chance that at least two brown sides come up?

New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to discuss difficulty levels, variations and alternate solutions, but plz. don’t publish the solutions. The solutions will be published after one or more weeks, and yes, we know that you are smarted than any one else.

You can check your solution here