**VERY EASY****A) **How many ways can we arrange **12 tiles** so that they form a **rectangle**?**B) **Get your calculator and try the following:

What do you get?**C) **The **A line** bus runs every **9 minutes** and the **B line** every **12 minutes**. If quite in line at the stop, how much it will take to re-match?**EASY****D) **Ana has a deck of **cards** and can make **groups of 2**, **3**, **and 5** without a **remainder letter**, what are the possible numbers of cards Her can have ?.**E) **We have a type of **brick** of dimensions:

How many bricks needed to build a **cube**?**F) **A type of cicada has a parasite whose **life cycle** is between** 2, 3** and **5 years**, this means that when the season ends and the parasite dies may take 2 3 or 5 years to reappear. What should be the life cycle of the cicada to not **match** this? (Based on a real case).**MEDIUM****G) **Divide the **clock** into **6 parts** so that all its parts **add up the same**.**E) **Participants in a parade can be in ordered in groups of **3**, **5 and 25** but can not do in groups of **4 **or **9**.

What is the number of participants if we know that between **1000** and **1250**?**H) **Given this imaginary situation of love:

How many laps will have to give **each wheel** for lovers touch again?.**HARD****I) **How to transport the **12 dogs** and **18 cats** so that all cages have to carry the **same number** of animals and cages are the largest possible.**Note**: No sane enough mix dogs and cats.**J) **We have a balance and **8 balls** of the same weight except for **one** that **weighs more**.

How many weighs have to do to know for sure **which is the** different **ball**?**VERY HARD****K) **Suppose **x** is any **prime** greater to 3. Show that its square gives a **remainder of 1** when divided by **12**.