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Today, Fatima is visiting her friend Ava. They have only recently become friends, and he wants to show her a custom of his family. On the table in front of them is a special-looking gyro on which the letters N, G, H and S are located (see picture)
Ava explains, "In the dark season, when autumn passes into winter, my family celebrates a special 8-day celebration. There is a tradition that we give away a roundabout and play with it. I'll give you this one."

 

 

Fatima looks at the roundabout with interest: "Thank you! And how do we play with it now?" Ava replies: "First, we look for some coins. Of the coins, we place some in the middle of the table and the others we divide among ourselves and place them in front of us. Then we take turns turning the gyro. When it falls over, one of the four letters points upwards. And this has a different meaning in each case:

- N means nothing: so you win nothing.
- G means Good: You win all the coins from the middle.
- H means half: you win half of the coins from the middle if the number of coins is divisible by 2. Otherwise, you won't win anything.
- S means Bad: You have to put one of your coins in the middle.

 

In the end, all coins won will be donated to a charitable cause."

 

After a few rounds, Fatima's eyes light up: "This is totally crazy! The gyro always falls exactly as I suspect!" Ava smiles, "Oh yes? Then prove it!"

Fatima thinks for a moment and looks at the gyro attentively: "Okay. In the middle are 24 coins. I bet I'll win exactly 7 coins from the middle in one of the next rounds." Ava laughs: "Well then, let's go, gyro whisperer. We continue to shoot alternately, you start. Let's see if you can do it."

 

How many times do the two have to spin at least for Fatima to win exactly 7 coins from the middle in one of their moves?

[Note: You have enough coins in your hand to be able to put more coins in the middle, even if you spin "Bad" frequently.]

a) 3 times (Fatima 2 times, Ava 1 time)
 b) 5 times (Fatima 3 times, Ava 2 times)
 c) 7 times (Fatima 4 times, Ava 3 times)
 d) 9 times (Fatima 5 times, Ava 4 times)
 

 
 Dec 5, 2021

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