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Write-up


Title
Common Digit

Problem Statement
 

All the numbers in the circle have something in common. There is a one-digit number that has the same thing in common with these numbers. What is the one-digit number? When you find out, place it in the circle.

 



Problem setup

All the numbers inside the circle have something in common.   What do they have in common?  Find a single digit that will also fit inside the circle.

 

Plans to Solve/Investigate the Problem

I will use the areas of number theory to discover the numbers' commonality.  That should lead me to the secret single digit in the center of the circle.

 

Investigation/Exploration of the Problem

The numbers are even, odd, prime, composite, 2-, 3-, and 4-digit numbers.  Divisibility rules for 2, 4, 5, and 10, do not show common traits.  How about adding up the digits to try for divisibility by 3 or 9?    Hey, the added value of the digits in each numbers adds up to 8.  There is the commonality!  And thus we have the single digit which should be placed in the center of the circle! 

 

Extensions of the Problem

>Find another set of numbers which share a different commonality.  Make sure there is a single digit number which will be a part of your solution. 

>Fill in a circle with numbers which share a commonality.  Add one more number which you think would be difficult to differentiate from the others.  Pass your circle on to another person to solve.

Author & Contact
rrogers@rockdale.k12.ga.us