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David and Albert are playing a game. There are digits from 1 to 9. The catch is that each one of them has to cut one digit and add it to his respective sum. The one who is able to obtain a sum of exact 15 will win the game? You are a friend of David. Do you suggest him to play first or second?
Difficulty Popularity There stand nine temples in a row in a holy place. All the nine temples have 100 steps climb. A fellow devotee comes to visit the temples. He drops a Re. 1 coin while climbing each of the 100 steps up. Then he offers half of the money he has in his pocket to the god. After that, he again drops Re. 1 coin while climbing down each of the 100 steps of the temple. If he repeats the same process at each temple, he is left with no money after climbing down the ninth temple. Can you find out the total money he had with him initially?
David to play second Explanation: Lets suppose that David plays first and he picks 9. Then Albert will definitely pick 8. Now, David will have to pick 7 or Albert will pick 7 in his turn. But if David picks up 7, then he will score 16 that is beyond 15 and will lose. So one thing is for sure, no one will be willing to start with the highest digits. Suppose David plays first and picks up 1, Albert will pick 2. Then David will pick 3 and Albert will pick 4. Now David will be forced to pick 9. The score is 6 to 13 and thus David will have no chance of winning. If David Picks 9 after Albert has picked up 2, then Albert will pick 8 and the score will become 10 to 10. Thus David will pick 3 as picking 7 will send him past 15. Now Albert will pick 4 and David has nothing to pick for winning. Thus Albert wins. Therefore, you should suggest David to play second. Submit your Email Address to get latest post directly to your inbox.
146900 Explanation: Whenever you face such type of questions, it is wise to begin from the last thing. Here in this question the last thing will be the 9th temple. He climbed down 100 steps and thus you know, he had Rs. 100 before beginning climbing down. Thus, he must have offered Rs. 100 to the god in that temple too (he offered half of the total amount). Also, he must have dropped Rs. 100 while climbing the steps of the ninth temple. This means that he had Rs. 300 before he begand climbing the steps of the ninth temple. Now, we will calculate in the similar manner for each of the temples backwards. Before the devotee climbed the eight temple: (300+100)*2 + 100 = 900 Before the devotee climbed the seventh temple: (900+100)*2 + 100 = 2100 Before the devotee climbed the Sixth temple: (2100+100)*2 + 100 = 4300 Before the devotee climbed the fifth temple: (4300+100)*2 + 100 = 8900 Before the devotee climbed the fourth temple: (8900+100)*2 + 100 = 18100 Before the devotee climbed the third temple: (18100+100)*2 + 100 = 36,500 Before the devotee climbed the second temple: (36500+100)*2 + 100 = 73300 Before the devotee climbed the first temple: (73300+100)*2 + 100 = 146900 Therefore, the devotee had Rs. 146900 with him initially.
Difficulty Popularity The puzzle is if the shopkeeper can only place the weights in one side of the common balance. For example: if shopkeeper has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names the weights you will need to measure all weights from 1 to 1000.