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.
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
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
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.
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