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)

Bongard dates (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 dates 1^*/*****

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

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, and 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 and here

Happy puzzling!

2020

It’s 2020, a new year! Here are a couple of 2020 related brainteasers:
1) 0-9!^**/*****
Make each and every of the numbers 0-9 by combining the four digits 2, 0, 2, and 0 with arithmetic and mathematical operators. For example 0*(2+2)+0=0

2) two different digits^**/*****
The year 2020 has only 2 different digits, 0 and 2. How many of those years do we have in this centur?

3) 0-9!^**/*****
And as a sequel on 2): how many such years are there in this millennium?

You can check your solutions 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.