This question is in the spirit of Guy's Strong Law of Small Numbers, and also the following two questions

Examples of patterns that eventually fail

Conjectures that have been disproved with extremely large counterexamples?

But with two extra conditions:

(1) The example should be at a primary school level (preferably restricted to the four operations of arithmetic) and,

(2) A pocket calculator could be used to convinced people of the correctness of the "fake pattern".

Why the conditions
I am writing something on a national maths textbook for teachers. I opened the textbook (for Year 3) and the first thing I found there was "Muliplication by $10$" asking students to use a calculoter to multiply a couple of one digit and two digits numbers by 10 and "discover" what they should do when multiply a number by 10. The purpose of the textbook was to use this obseravation to teach how to multiply a one digit number by a two or three-digit number. Meanwhile stduents LEARN that "You can tell by looking" right at the early years of their schooling.

Here is one example from Guy's The Second Strong Law of Small Numbers that I am probably going to use.

A Niven Number has been defined as one which is divisable by the sum of its decimal digits, such as 21 and 133. Is $n!$ always a Niven number?

Of course, I am going to modify the languge of the question for my purpose (e.g., dropping the notation of the factorial), and also rewrite it in a calculator friendly way (e.g., find the reminder when $24 (=2.3.4)$ is divided by $6(=2+4)$.)

If you have an example to suggest, you do not need to concern yourself with the modifications, I find my way. Of course, you are welcome to suggest your way, in particular when it comes to the use of pocket calculators.



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