I hope this is the correct category to post. Please do not give away the answer here if you know it. Message me instead or just be happy that you figured it out. But there is more than one answer.
You will need a calculator or phone and a few minutes time. To keep it fun I will change the ending for every new participant. Start by clearing the calculator. Type in a single digit number besides 1 or 0 they are no fun. Multiply key than another. Do it again. Keep going until you have at least 8 digits or more. The = key is optional. There are only a few rules to follow if you don’t it’s cheating. You cannot type the same number more than 2 times in a row. You cannot go back and forth between 2 or 3 different numbers. You have to use most of the 10 digits available, but not necessarily all of them. Use the top and bottom of the rectangular keypad. The left and right side. This happens automatically without even trying after 20 cycles. It’s ok if you break this rule by mistake. Just don’t do it on purpose. Let’s start by choosing random digits. No planning or thinking. Type the result here leaving out the 100’s place. The 3rd from the end. Put an X or period instead like this.
6372836712X89
Do not type the missing digit.
If you don’t cheat there is no reason to record your key presses. If it’s random I will accept your word. If you plan or choose your digits in later rounds then record them, along with your answer, to prove you didn’t break the rules when I catch you. Just type your answer here then we’ll do the next step. One at a time please you can follow along. Who is first?
Following your rules (I don’t have a rectangular keypad but I know what numbers are on it), there’s only one way I know of to break it, but I’ll be nice, and choose a different number.
505774x80
(Even here, though, I think your odds of guessing my # are only 50/50).
It’s magic! Next I want you to lie or tell the truth. But you must choose from the even numbers 24680. Tell me your missing number X. I will say for certain if you’re telling the truth.
There’s a statistical tendency for the ever-growing product to grow an ever-growing set of trailing zeros. By the time it’s 8 digits long it it very likely to have 1 or 2 trailing zeros that won’t go away as the product continues to grow.
Any combination with at least 2 even numbers and 2 5s, or 2 5s and a 4 or 8, will end up with a multiple of 100. Multiples of 1,000 will result if there are 3 5s and a smattering of evens.
I’m happy to help you polish the trick, but if folks aren’t doing it right, you may need to reframe it.