In this dystopian world, your resistance group is humanity's last hope. Unfortunately, you've all been captured by the tyrannical rulers and brought to the ancient colosseum for their deadly entertainment. Before you're thrown into the dungeon, you see many numbered hallways leading outside. But each exit is blocked by an electric barrier with a combination keypad. You learn that one of you will be allowed to try to escape by passing a challenge while everyone else will be fed to the mutant salamanders the next morning. With her perfect logical reasoning, Zara is the obvious choice. You hand her a concealed audio transmitter so that the rest of you can listen along. As Zara is led away, you hear her footsteps echo through one of the hallways, then stop. A voice announces that she must enter a code consisting of three positive whole numbers in ascending order, so the second number is greater than or equal to the first, and the third is greater than or equal to the second. She may ask for up to three clues, but if she makes a wrong guess, or says anything else, she'll be thrown back into the dungeon. For the first clue, the voice says the product of the three numbers is 36. When Zara asks for the second clue, it tells her the sum of the numbers is the same as the number of the hallway she entered. There's a long silence. You're sure Zara remembers the hallway number, but there's no way for you to know it, and she can't say it outloud. If Zara could enter the passcode at this point, she would, but instead, she asks for the third clue, and the voice announces that the largest number appears only once in the combination. Moments later, the buzz of the electric barrier stops for a few seconds, and you realize that Zara has escaped. Unfortunately, her transmitter is no longer in range, so that's all the information you get. Can you find the solution? Pause on the next screen to work out the solution. 3 2 1 You're worried about the fact that you don't know Zara's hallway number, but you decide to start from the beginning anyways. From the first clue, you work out all of the eight possible combinations that come out to a product of 36. One of these must be right, but which one? Now comes the hard part. Even though you don't know which number you're looking for, you decide to work out the sum of each combination's three numbers. That's when it hits you. All but two of the sums are unique, and if the hallway number had matched any of these, Zara would have known the correct combination right then and there without asking for the third clue. Since she did ask for the clue, the hallway number must have matched the only sum that appears more than once in the list: thirteen. But which of the two combinations that add up to thirteen is correct: 1,6,6, or 2,2,9? That's where the third clue comes in. Since it tells us that the largest number must be unique, 2,2,9 must be the code. When night falls, you and the others escape through hallway thirteen and rejoin Zara outside. You've freed yourselves through math and logic. Now it's time to free the rest of the world.
在這個反烏托邦世界中, 你的反抗團隊是人類的最後希望 不幸的是, 你們被暴政統治者悉數抓獲 被帶到古代鬥獸場, 將與野獸死亡搏鬥以娛樂他們 被關進地牢之前, 你看到許多通往外界 且帶序列號的通道 但每個出口都被配備有 密碼鍵盤的電柵擋住 只有輸入正確但密碼才可通過 你被告知其中一人將被允許 試著通過一項挑戰而逃脫 其他人則會於次日 成爲變種火蜥蜴的早餐 Zara 邏輯推理很強,很明顯是最佳人選 你遞給她一只隱藏音頻發射器, 所以你們能監聽全程 Zara 被帶離牢房時 你們聽見她的腳步聲 在其中一個通道中迴盪 然後停了下來 一個提示音響起,她必須輸入一個密碼 密碼是三個由小到大的正整數組成 也就是說, 第二個數字大於或等於第一個數字 第三個數字大於或等於第二個數字 她最多可以問三個提示 但如果她猜錯密碼 或說了無關緊要的話 她將被重新關進地牢 第一個提示:三個數字相乘得36 Zara 問了第二個提示 它是:數字的總和 是 Zara 走進的通道編號 接著是一陣沉寂 你知道 Zara 一定記得通道的號碼 但你們無從得知 她也無法大聲告知你們 如果 Zara 已經推理成功, 她將會輸入密碼 但是,她詢問了第三個提示 第三個提示:最大的數字 僅出現一次 過了一會兒,電柵欄的聲音消失了幾秒 你們意識到Zara已經成功逃脫了 不幸的是, 她的音頻發射器超出接受範圍 所以這是你們僅有的線索 你們能找到最終答案嗎? 按下暫停鍵,好好想一想 3 2 1 你擔心你不知道Zara走的通道編號 不過,你還是打算重頭開始 根據第一個提示, 你找出 8 個可能的組合 都符合數字相乘等於36 其中一個是正確答案,是哪個呢? 現在是最難的部份 即使你不知道哪個是正確的 你仍然決定把每個組合的總和算出來 這個決定讓你靈光乍現 除了兩組外,其它組的總和都只出現一次 如果通道號碼與其中任何一個數字一致 那麼當時Zara應該能輕而易舉地得出答案 並不需要第三個提示 然而,她詢問了第三個提示 因此,通道號碼肯定是 那個總和出現不止一次的數字: 13 但總和為 13 的兩組中,哪個是正確的: 1,6,6 還是2,2,9? 這時,你需要第三條提示來確定答案 最大的數字僅出現一次 因此答案是 2,2,9 夜晚降臨, 你與其他同伴沿著通道 13 順利逃脫 在外與 Zara 重逢 利用數學和邏輯,你們重獲自由 現在是解放全世界的時刻了