Bongard dates (4)


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.

1)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.

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.

Happy puzzling!

Six sixes


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.

Bongard dates (3)


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.

1)Bongard problem dates 5***/*****

2)Bongard problem dates 6****/*****

The original Bongard problems were geometrical and thus, in theory, culture free. These dates are western dates, and thus not culture independent. I have used the Italian/Dutch format. 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. During my recent visit to Burkina Faso I wrote up 12 problems, so I have enough to trouble you the first half of 2020.

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.

Happy puzzling!

Bongard letters (1)


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.

1)Bongard problem letters 1*/*****

2)Bongard problem letters 2**/*****

Though I’m in the midst of a series Bongard problems on Dates and times, I throw in a couple on letters just for a change.

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 and here

Happy puzzling!

Five five’s



Some of you may know the problem to make all the numbers from 1 to 20 with four fours.
I wrote about it here. It may come as a surprise to you that it is possible to make all the numbers from 0 to 100.

Today’s problem is to make all numbers from 0 to 20 using exactly five fives. For example:
(5*5 – 5*5) / 5 = 0

You can find my solutions here.

Squirrels go nuts


When I returned from Burkina Faso early January, my wife presented me with a copy of Smart Game’s new “Squirrels go Nuts!” puzzle.

I already had several of Smart Games puzzles, such as “IQ link” and “IQ Fit”, and they usually provide a decent amount of puzzles, starting easy and gradually toughening. This one is no different.

The puzzle consists of a tray with four holes, and four squirrels who have to drop their acorn into one of the four holes. Your task is to slide the squirrels over the board so that the acorns are dropped into a hole.

The puzzle comes with a booklet with 60 problems, and you may wish to skip the first half of them – personally I found them ridiculously easy, and no, I’m not a super genius.

Bongard dates (2)


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.

1)Bongard problem dates 3*/*****

2)Bongard problem dates 4*/*****

The original Bongard problems were geometrical and thus, in theory, culture free. These dates are western dates, and thus not culture independent. I have used the Italian/Dutch format. 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. During my recent visit to Burkina Faso I wrote up 12 problems, so I have enough to trouble you the first half of 2020.

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

Happy puzzling!

Three cubes


In the picture above, when we calculate the sum of the three cubes on the left side, we see that two of the digits are present in the sum.

There are no 2-digit numbers which are equal to the sum of the squares of their digits.
There are 3-digit numbers which are equal to the sum of their third powers. Which are they?

(My sincerest apologies for not providing a link to a solution. WordPress has changed the interface and I have been unable to master it. I’m still looking for the right way to switch to html editing and add images and links)