1999 CEMC Pascal Problems/Problem 13
Problem
In Circle Land, the numbers 
and 
are shown in the following way:
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In Circle Land, what number does the following diagram represent?
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Solution 1
Using the first two provided diagrams, we can see that the rings represent what place a specific number is in, or what. For example, if a number has two rings around it, then that number represents the hundreds digit and would be multiplied by 
, while a number with five rings around it would represent the hundred thousands digit, and would be multiplied by 
.
Using this, we can count the number of rings around each number for the number that we are trying to find. 
has four rings around it, so there must be a in the ten thousands place. 
has two rings around it, so there must be a in the hundreds place. 
has no rings around it, so the must be in the The rest of the digits in the number must be 
.
The number that corresponds to this is 
~anabel.disher
Solution 2 (answer choices)
We can use the same logic from solution 1. However, we can eliminate answer choices.
Since must be in the ten thousands place, we can eliminate answer choices C, D, and E, leaving only answer choices A and B.
We can now see that must be in the ones place because it doesn't have any rings around it. This means that must be the answer.
~anabel.disher
Solution 2.5
Rather than comparing the ones digits of answer choices A and B, we can compare the tens place.
In the diagram, we can see that there are no numbers that have only one ring around them, which would correspond to the tens place. This means that must in the tens place, which means that answer choice is the answer.
~anabel.disher
