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keisanHigh-precision calculations for everyday life and work

Math Magic (What’s left when you add six numbers one after another?)

Author: tonagaiExecutions: 6003

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Write down any six numbers of your choice. Then, write the first digit of the sum of each pair of adjacent numbers one row below.
Repeat this process, and the final number that appears is the one you’ll guess the moment you finish writing the six numbers—it’s a math magic trick.
(From a tweet by Jun Mitani)
First one
Second one
The third one
The fourth one
Fifth
The sixth one
What happens if you add the second and fifth numbers? 
You can already guess it at this point. If the number is even, add the first and sixth digits; if it is odd, add 5 to that sum and take the first digit of the result.
The six numbers you entered      
Add the adjacent numbers to get the first digit     
Add the adjacent numbers to get the first digit    
Add the adjacent numbers to get the first digit   
Add the adjacent numbers to get the first digit  
Finally... 
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