A circle is divided into 5 equal slices. In each figure, x slices are removed, and the remaining slices form a pattern that corresponds to a number. Observe the following:

Figure 1:When 2 slices are removed, the remaining pattern corresponds to 211. Figure 2: When I slice is removed, the remaining pattern corresponds to 1023.

When 0 slices are removed, what number will the remaining figure represent?

Question

A circle is divided into 5 equal slices. In each figure, x slices are removed, and the remaining slices form a pattern that corresponds to a number. Observe the following:

Figure 1:When 2 slices are removed, the remaining pattern corresponds to 211. Figure 2: When I slice is removed, the remaining pattern corresponds to 1023.

When 0 slices are removed, what number will the remaining figure represent?

Quintessence Classes · Accepted Answer

The correct answer is 3125. The pattern is formed by taking the number of remaining slices raised to the fifth power (the total number of slices) and subtracting the number of removed slices raised to the fifth power.Figure 1 (2 slices removed, 3 remaining):Three to the power of five is two hundred forty-three. Two to the power of five is thirty-two. Two hundred forty-three minus thirty-two gives 211.Figure 2 (1 slice removed, 4 remaining):Four to the power of five is one thousand twenty-four. One to the power of five is one. One thousand twenty-four minus one gives 1023.Target Figure (0 slices removed, 5 remaining):Five to the power of five is three thousand one hundred twenty-five. Zero to the power of five is zero. Three thousand one hundred twenty-five minus zero gives 3125.

Answer

7776

Answer

6561

Answer

2401

Answer & Explanation

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