Realising he needs money, Tintin reaches inside the bank situated on the island, and sees a row of lockers which start with 0 and go on till infinity. A locker can contain any number of coins. A coin is placed in the locker with index 7 (i.e. the 8th square). The aim is to move this coin to the locker with index 1. (i.e. the 2nd square) and all other squares empty. There are two rules to this: 1) Fission Rule: A coin may be replaced by a pair of coins by placing one in each of the immediately adjacent squares. Eg. Coin #3 can be replaced by Coin`#2` and Coin`#4` where Coin#(number) rep- resents coin in position with index number. 2) Fusion Rule: A pair of coins separated by exactly one intervening square can be replaced by a single coin in that middle square. Eg. Coin`#2` and Coin`#4` can be replaced by Coin#3. Minimum number of moves required to achieve our aim ?A. 18B. 19C. 17D. 16

Realising he needs money, Tintin reaches inside the bank situated on t

1.	Realising he needs money, Tintin reaches inside the bank situated on the island, and sees a row of lockers which start with 0 and go on till infinity. A locker can contain any number of coins. A coin is placed in the locker with index 7 (i.e. the 8th square). The aim is to move this coin to the locker with index 1. (i.e. the 2nd square) and all other squares empty. There are two rules to this: 1) Fission Rule: A coin may be replaced by a pair of coins by placing one in each of the immediately adjacent squares. Eg. Coin #3 can be replaced by Coin`#2` and Coin`#4` where Coin#(number) rep- resents coin in position with index number. 2) Fusion Rule: A pair of coins separated by exactly one intervening square can be replaced by a single coin in that middle square. Eg. Coin`#2` and Coin`#4` can be replaced by Coin#3. Minimum number of moves required to achieve our aim ?A. 18B. 19C. 17D. 16
Answer» This puzzle seems rather difficult to solve by trying random moves that appear to get one closer to the solution. However, consider the board a sequence of integers, each being the number of pennies at that location, and the moves as adding or subtracting (+1, 1, +1) to three consecutive values. Then by inspection we can come up with a solution, not worrying about whether the number of pennies is always positive, by adding the columns: 0 0 0 0 0 0 +1 (start) 0 0 0 0 1 +1 1 0 0 0 1 +1 1 0 0 +1 1 +1 0 0 0 +1 1 +1 0 0 0 0 +1 0 0 0 0 0 0 (end) This gives you the four critical moves that must be in any solution. However, applying them directly is illegal. [But you can] just [keep] splitting the left penny (7 times), then [do the] “critical 4 moves” and you come up with the mirror image position, so you now combine to the final position. Ergo, 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 2 1 1 1 1 1 lt +1 1 +1 1 1 1 1 2 1 1 1 1 lt +1 1 +1 1 1 1 1 1 2 0 1 1 1 1 1 1 1 1 1 0 1 lt 1 +1 1 1 1 1 1 1 1 0 1 0 lt 1 +1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

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You and your friend save as much money as possible by participating in the contest and fly to Athens. Exploring Athens you and all other teams come to Parthenon, the temple of Athena, who is the goddess of wisdom and intelligence. You also see many images of an owl. You learn from the guide that it is the “Athena Noctua”, also called the Minerva owl or the little owl. The guide also mentions some interesting stories of Athena’s wisdom and cleverness. The tourist guide at Parthenon takes you to an abandoned tunnel. And here you find an inscribed stone and a bowl of colored flowers. Suddenly you hear a deep and ancient gong ringing as you start reading the Stone Of Instructions. The instructions read as follows: Every person entering the Temple of Athena will be given a bowl with 15 red flowers and 12 yellow flowers. Each time the Gong of Time rings, he/she must do one of two things: 1. Exchange: If he has at least 3 red flowers in his bowl, then he may exchange 3 red flowers for 2 yellow flowers. 2. Swap: He may replace each yellow flower in his bowl with a red flower and replace each red flower in his bowl with a yellow flower. That is, if he starts with i red flowers and j yellow flowers, then after he performs this operation, he will have j red flowers and i yellow flowers. [You can leave the tunnel only when you make all the combinations (no. of red, no. of yellow) of flowers that are possible]. What is the number of combinations you need to make to leave the tunnel?A. 27B. 52C. 54D. None of these
You and your friend save as much money as possible by participating in the contest and fly to Athens. Exploring Athens you and all other teams come to Parthenon, the temple of Athena, who is the goddess of wisdom and intelligence. You also see many images of an owl. You learn from the guide that it is the “Athena Noctua”, also called the Minerva owl or the little owl. The guide also mentions some interesting stories of Athena’s wisdom and cleverness. The tourist guide at Parthenon takes you to an abandoned tunnel. And here you find an inscribed stone and a bowl of colored flowers. Suddenly you hear a deep and ancient gong ringing as you start reading the Stone Of Instructions. The instructions read as follows: Every person entering the Temple of Athena will be given a bowl with 15 red flowers and 12 yellow flowers. Each time the Gong of Time rings, he/she must do one of two things: 1. Exchange: If he has at least 3 red flowers in his bowl, then he may exchange 3 red flowers for 2 yellow flowers. 2. Swap: He may replace each yellow flower in his bowl with a red flower and replace each red flower in his bowl with a yellow flower. That is, if he starts with i red flowers and j yellow flowers, then after he performs this operation, he will have j red flowers and i yellow flowers. [You can leave the tunnel only when you make all the combinations (no. of red, no. of yellow) of flowers that are possible]. After how many operations will you have 5 each of red and yellow flowers?A. 5B. 10C. 15D. None of these
After winning the challenge fair and square, and winning a Snorlax, Max finally reaches Viridian City. As he enters viridian city, he notices that there is a Pokémon trainer in front of the gym. I will only let you pass if you beat me in my favourite game, he says. This is a game played with a sequence of tiles, each labelled with two numbers. You start at the first the in the sequence and choose one number from each tile that you stop at, according to the following rules: • At tile i, if you pick up the smaller number, you move on to the next tile, i+1, in the sequence. • At tile i, if you pick up the larger number, you skip the next tile and move to tile i+2 in the sequence. The game ends when your next move takes you beyond the end of the sequence. Your score is the sum of all the numbers you have picked up. For example, suppose you have a sequence of four tiles as follows: Then the maximum score you can achieve is 3, by choosing the numbers that are circled. Now, you are given the following tiles. What is the maximum score you can make to ensure you beat the security guard?
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