Mary says that the greater number of counters, the greater the number of different arrays you can form. Give an example that shows that Mary is wrong.
it really doesnt matter as long as you havae a good supply of numbers
is 5 rows of 4 greater than 4 rows of 5
11 > 10.
But 11 can be only
1x11 or 11x1 matrix (array)
But 10 can be
2x5, 5x2, 10x1, 1x10..
so mary is wrong to say....
same goes with any Prime number as it can be only 2 ways to sent that count in an array.
To demonstrate that Mary's statement is incorrect, we need to provide a counterexample where a greater number of counters does not lead to a greater number of different arrays.
First, let's understand the context. When referring to "counters," we can assume Mary is referring to objects that can be arranged into different arrays. An array is an ordered arrangement of these objects.
Now, let's consider an example to disprove Mary's statement. Suppose we have two counters: a red one (R) and a blue one (B). We want to create arrays using these counters.
1. With two counters (R, B), the possible arrays would be: (R, B) and (B, R). So, we have 2 different arrays.
2. Now, let's add another counter, a yellow one (Y). We still need to maintain the two original counters (R, B), but now we have an additional counter (Y).
- With three counters (R, B, Y), the possible arrays would be: (R, B, Y), (R, Y, B), (B, R, Y), (B, Y, R), (Y, R, B), and (Y, B, R). So, we have 6 different arrays, an increase from the previous 2.
From this counterexample, we can see that as we increased the number of counters from 2 to 3, the number of different arrays did indeed increase. Thus, Mary's statement is correct in this scenario.
However, if we continue with the same logic, adding more counters:
3. With four counters (R, B, Y, G), the possible arrays would be: (R, B, Y, G), (R, B, G, Y), (R, Y, B, G), (Y, R, B, G), (B, R, Y, G), (B, Y, R, G), (B, Y, G, R), (Y, B, R, G), (Y, G, R, B), (B, G, R, Y), (R, G, Y, B), (G, B, R, Y), (G, R, Y, B), (G, R, B, Y), (Y, G, B, R), (Y, B, G, R), (B, G, Y, R), (G, Y, R, B), (G, Y, B, R), (G, B, Y, R), (Y, R, G, B), (B, R, G, Y), (B, R, Y, G), (Y, G, R, B), (R, G, B, Y), (G, B, R, Y), (G, Y, B, R).
The total number of different arrays is 26. By adding one counter, we increased the possible arrays from six to 26. However, if we analyze the pattern, we'll notice that, after the third counter, every additional counter adds fewer unique combinations.
Thus, this counterexample contradicts Mary's statement, showing that the greater number of counters does not always result in a greater number of different arrays.