Beaver Sofia and her group of friends are playing a game called 'Lights On.'海狸索菲亚和她的朋友们正在玩一个叫“开灯”的游戏。
The game has 8 large buttons which, when stood upon, send a signal down a wire.该游戏有 8 个大按钮，踩上去就会通过电线发出信号。
These wires pass through some triangular or square boxes before eventually reaching a light bulb.这些电线在最终通向灯泡之前，会穿过一些三角形或方形的盒子。
- A triangle will only send a signal if BOTH incoming wires send it a signal.一个三角形只有在两条输入线都向其发送信号时才会发送信号。
- A square will send on a signal if only ONE of the incoming wires send it a signal.如果仅有一根输入线向一个方块发送信号，那么该方块就会发送信号。
- The friends win the game if they can turn the light on.如果朋友们能打开灯，他们就赢得比赛。
Task:任务:
Select which buttons the beavers could stand on to turn on the light and win the game. 选择海狸可以踩踏的按钮，以点亮灯光并赢得游戏。
(Click on the switches to place and remove beavers. Press 'Save' when you have finished.)（点击开关放置和移除海狸。完成后按“保存”。）
Explanation 解释
Answer: 答案:
There are 16 possible combinations of the 8 buttons that will turn the light-bulb on. One is shown below:有 8 个按钮的 16 种可能组合可以点亮灯泡。其中一种组合如下所示：
Explanation: 解释:
A good approach to this question is to work backwards. The light-bulb at the end is connected to a wire in column 4 that comes from a triangle. For this wire to be ON, we know that the two wires leading into the triangle must also be ON.解决这个问题的一个好办法是从后往前推。最末端的灯泡与第 4 列的一根导线相连，这根导线来自一个三角形。要使这根导线处于接通状态，我们知道通向这个三角形的两根导线也必须处于接通状态。
These wires are connected to a triangle and a square.这些电线连接着一个三角形和一个正方形。
We know this triangle must be ON, therefore the wires connecting to it must both be ON.我们知道这个三角形一定是亮着的，所以连接到它的两根线也一定是亮着的。
We know the square must be ON, therefore one of the wires connecting to it must be ON, and the other must be OFF.我们知道这个方块一定是亮着的，所以连接它的两条线中必有一条是亮着的，另一条是熄灭的。
For columns 1 and 2, we will look at the wires in the top half and bottom half separately.对于第 1 列和第 2 列，我们将分别查看上半部分和下半部分的电线。
Top half:
Both wires in column 2 must be ON. Therefore, the top 2 buttons in column 1 must be pressed, and exactly one of the buttons of the bottom 2 buttons must be pressed. 上半部分:第二列的两根电线都必须接通。因此，第一列的上面两个按钮必须按下，而下面两个按钮中必须且只能按下其中一个。
Bottom half:
Given the square is in the ON position, exactly one of the wires leading into it must be ON, and the other is OFF. Therefore, either the triangle leading into it must be ON and the square OFF or vice versa. There are multiple ways of doing this - the solution shown above demonstrates one possible approach. Here, the triangle is ON and therefore the top two buttons must be pressed, meaning the square must be OFF and the bottom two buttons are either both pressed or not pressed (in this case, both are not pressed). 下半部分:鉴于正方形处于开启状态，进入它的两条线中必有一条开启，另一条关闭。因此，进入它的三角形要么开启而正方形关闭，要么相反。实现这一目标的方法不止一种——上面展示的解决方案只是其中一种可能的途径。在此，三角形开启，所以上面的两个按钮必须按下，这意味着正方形关闭，而下面的两个按钮要么都按下，要么都不按（在这种情况下，两个按钮都没有按）。
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