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# Secrets of the Mystery Calculator

Tracey Mahler on Flickr

Ready to read some minds? Nothing to it with the Mystery Calculator.

The Mystery Calculator is a pack of six cards that have rows of numbers on them. Show the cards to your friend and ask them to pick one number on one card and then pick all of the other cards that have that number and hand them over to you. Once you have the cards you can deduce what number your friend picked.

Magic? Not quite. Just math. The trick is to add up the top left number on each card that was given to you and you’ll have your answer. The only magical thing is that you will be doing calculations just like a computer.

The top-left numbers on the cards create a 32-bit calculator that converts binary representations to real decimal numbers and vice versa. So here’s how it works. When we count, we use a system called “base 10.” It sounds complicated, but you’ve been counting using it your whole life. “Base 10” just means that when you add another digit to a number, the new digit is 10 times bigger than the one before it.

So, when we have a single digit number (1-9), that digit represents single units. When we make it a two-digit number (10-99), the next number is ten times the units of the previous digit: 10 multiplied by 1 is 10. A third digit (100-999) is ten times the second one: 10 multiplied by 10 is 100.

For example, when you see the number 356, you see it as three 100s, five 10s, and six 1s. Add them up, and you have 356!

Computers, on the other hand, process data in 1s and 0s. They can’t write out ‘356’ as we do, because 3, 5, and 6 are all higher than 1. To count to higher numbers, it has to use base 2. Base 2 is like base 10, but instead of the next number being ten times bigger, it’s two times. So, instead of 1, 10, 100, etc, it goes 1, 2, 4, 8, 16, 32, and so on. That means that in base 2, 101011 is one 1, one 2, one 8, and one 32; add them up and you get 43. Remember that the rightmost number is the smallest, just like a base 10 number.

So, how does this apply to the Mystery Calculator? Well, if you look at the top left number of each card, you’ll find a 1, 2, 4, 8, 16, or 32. This enables you to count in binary up to 32 just like a 32-bit calculator. The cards are set up so that whatever number the person chooses will appear on all the cards that add up to that number. Say you pick the number 43. The cards that have 43 on them will be the ones in which those top left numbers (in this case, 1, 2, 8 & 32) will add up to 43 and that’s where the magic happens.

#### How the Mystery Calculator works

https://mathsedideas.blogspot.com/2017/12/on-christmas-cracker-mystery-calculator.html

#### Digital mystery calculator

https://eddmann.com/mystery-calculator-clojurescript/