A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

Question

In the 2020 summer Olympics' Javelin throw finals, Neeraj Chopra exhibited a spectacular performance to win the gold medal. The silver medal was won by Jakub Vadlejch and the bronze medal was won by Vitezlav Vesely. There were six rounds of throws with each athlete having one throw per round. The best of all the throws of each athlete is considered for the medal. Following were the observations about the throws:
(i) The first and second rounds were dominated by Neeraj Chopra with a gold medal performance in his second throw, while the other two athletes did not have any medal winning throws in these rounds.
(ii) The throws in the last round by both Jakub Vadlejch and Vitezlav Vesely were fouls and were not considered for scoring.
(iii) After four rounds, Vitezlav Vesely was in the second position and could not improve upon his best throw in the succeeding rounds.
(iv) In the fourth round, the throw by Jakub Vadlejch was the best in that round.
In which round did Vitezlav Vesely have his best throw?

Answer 1

Step 1: Understanding the Question:
We must decide which of the two drawn cubes, (i) or (ii), could really result from folding the six-square net in Panel I along its marked dashed creases.

Step 2: Key Formula or Approach:
A clean way to test this is the "three faces at one corner" rule: on a real cube, three faces meet at every corner, and the fold lines in the net already tell us which three faces meet at each corner and how they are rotated relative to one another. If a drawn cube shows a corner where the shading pattern could not have come from three faces of the net meeting in that fixed rotation, that cube is fake.

Step 3: Detailed Explanation:
Picking the hub face C as the front of the cube fixes the layout: the square above it (T) becomes the top, the one below it and the square below that (D1, then D2) wrap around to become the bottom and the back, and the two side squares (L and R) become the left and right faces. This also tells us D2 (fully gray) sits opposite the plain white C, T sits opposite the plain white D1, and L (mostly gray with a white notch) sits opposite R (mostly white with a gray patch). Now look at what each cube in Panel II actually shows. Cube (i) mixes a partly-shaded top, a notched gray face, and a split side face in a combination where the solid-gray face (D2) never appears in full and the plain-white opposite pair (C) is also missing, so the three faces visible in (i) cannot be three genuine faces of the net meeting at a shared corner in the required rotation. Cube (ii), by contrast, shows one full solid gray face together with a plain white face and a single diagonally shaded face, which is exactly the kind of trio the net produces once D2 is turned to face up: D2 solid gray on top, its neighbour D1 (plain white) on one visible side, and a corner-shaded face such as T or R on the other visible side.

Step 4: Final Answer:
Only cube (ii) shows three faces that genuinely correspond to a valid corner of the folded net, so the correct choice is option (B), only (ii).

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

Show Hint

The Correct Option is B

Solution and Explanation

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