Quento

October 2, 2020ArithmeticTeun Spaans

While cleaning up old newspapers in someone’s house I came across a puzzle called “Quento” in the Dutch newspaper “Algemeen dagblad”.

The basics of this puzzle are simple calculations. What sets it a bit apart from other puzzles is that the answers are given, and that you have to find the exercise.

Example:

You have to find a calculation for each of the numbers on the right by going from a number to a + or – sign and on to another number. If necessary, you may add additional +/- signs and numbers, as long as you don’t use the same number or sign twice.

What you may do:

Not allowed is:

Of course there is a website, and an app for both Android and Ipad. Personally I think the exercises are too easy, though no doubt they can be increased by adding size and moving to higher numbers, as shown in our 4th problem. In the app I did see higher numbers, in the sense of multiples of 3, 4, 5 , and so on, but I didn’t see larger sizes, as in our fourth problem. That may be because I didn’t purchase the app and just used the free version.

Quento 2^*/*****

Quento 3*/*****

Quento 4**/*****

You can check your solutions at href=”https://justpuzzles.wordpress.com/Solutions to puzzles 501-750/#516″>here.

Dutch double true alphametics

September 18, 2020alphameticTeun Spaans

An alphametic is an addition in words, verbal arithmetic. It is a puzzle in which you have to replace the letters by digits, and get a correct calculation.
This Friday I bring you a number “double true” alphametics from the dutch language.

1) Three^**/*****
EEN + EEN + EEN = DRIE

2) Six^*/*****
EEN + EEN + EEN + EEN + EEN + EEN = ZES

3) Seven^**/*****
TWEE + TWEE + EEN + EEN + EEN = ZEVEN

4) Nine^***/*****
DRIE + DRIE + DRIE = NEGEN

5) Thirty (1)^**/*****
TWAALF + ELF + DRIE + TWEE + TWEE = DERTIG

6) Thirty (2)^***/*****
ELF + NEGEN + TWEE + TWEE + TWEE + TWEE + TWEE = DERTIG

Though you don’t need them, here is the list of Dutch counting words:
1 Een
2 Twee
3 Drie
4 Vier
5 Vijf
6 Zes
7 Zeven
8 Acht
9 Negen
10 Tien
11 Elf
12 Twaalf
13 Dertien
20 Twintig
30 Dertig

New puzzles are published at least once 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 solutions here

Lyfoes

September 4, 2020UncategorizedTeun Spaans

New puzzle types are often an variation on an existing theme or situation.

Take for example the Towers of Hanoi. Citing wikipedia: It consists of three rods and a number of disks of different sizes, which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.

The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:
* Only one disk can be moved at a time.
* Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
* No larger disk may be placed on top of a smaller disk.

A new variation on this puzzle is Lyfoes. The stacks have been replaced with tubes, and the disks have been replaced with coloured balls. Initially there are one or two empty tubes, and the coloured balls are all mixed up. The object is to sort the balls according to colour.

Example of start:

The app has 5 difficulty levels, from very easy to insane.
Well worth a look.

Write

August 21, 2020UncategorizedTeun Spaans

Replace letters by digits to obtain a correct summation. The same letters always represents the same digit.

1) Pencil^***/*****
WRITE
REPORT
——+
PENCIL

2) Pencil^****/*****
NOTE
MEMO
PAPER
WRITE
—–+
REPORT

Happy puzzling!

Jewelry

July 17, 2020CryptarithmTeun Spaans

This Friday the return of a puzzle type we haven’t seen for a while:

1) Jewelry^****/*****
OPALS
CORAL
LAPIS
—–+
TIARA

Replace every letter by a digit to get a correct addition. A letter always represents the same digit.

Happy puzzling!

Four of a kind

July 3, 2020CombinatoricsTeun Spaans

This weeks puzzle I came across in an old issue of ‘Machazine’, dated July 2017.

How many cards should I draw from a double deck of cards to make sure I hold at least one four of a kind?

Bongard dates (5)

June 19, 2020Bongard problems, Inductive reasoningTeun Spaans

In 1967 the Russian scientist M.M. Bongard published a book containing 100 problems. Each problem consists of 12 small boxes: six boxes on the left and six on the right. Each of the six boxes on the left conforms to a certain rule. Each box on the right contradicts this rule. Your task, of course, is to figure out the rule.

Bongard problem dates 9^***/*****

2)Bongard problem dates 10^*/*****

The original Bongard problems were geometrical and thus, in theory, culture free. These dates are western dates, and thus not culture independent. The 2-weekly puzzle column in the Guardian in the past already expanded the scope from geometry to language, but as far as I know the dates are a new territory.

Happy puzzling!

Four fruits

June 5, 2020AlgebraTeun Spaans

Recently I noticed a lot of elementary algebra represented as pictures. Personally I doubt that packing exercises in this format helps the learning process, but if people like it as a puzzle, here is an example (with a little twist, of course)

1) Four fruits^{*/*****>/sup>}

What do an apple and a cherry cost me?

Bongard dates (4)

May 15, 2020Bongard problems, Inductive reasoningTeun Spaans

1)Bongard problem dates 9^**/*****

2)Bongard problem dates 10^*/*****

Six sixes

April 24, 2020ArithmeticTeun Spaans

Digits and numbers are wonderful toys. The number of problems with them surpasses the imagination. Still, great minds think alike.
In 2013 I posed a classical problem to make as many numbers as possible by combining four fours.

In March I posed the challenge to make all the numbers of 0 to 20 by combining 5 5’s.

1) 6 6’s^***/*****
Today’s problem is a sequel: make all the numbers 0 till 20 using 6 6’s. You can use brackets, +,-,*,/, ^and sqrt. You msy use ! for just one of the numbers.
You can check your solutions here and here

When googling, I found the puzzle masters at occupymath have posed the same challenge.

2) 7 7’s^***/*****
Of course the problem can be generalized to 7 7’s. Make all numbers 0-24 using seven sevens, brackets, +-*/, no faculty.
You can check your solutions here and here

3) general ^***/*****
The next problem is not, as you may have thought, to make all numbers 0-20 with 8 8’s. Rather the question is, can the numbers 0-20 with made with all digits? In base 11, in base 12?
For a start:
0 = (n-n)*(n+…+n)
1 = n/n + (n-n)*(n+…+n)
2 = n/n + n/n + (n-n)*(n+ … + n)
and so on.