Our group consists of:

Marina, Zoe and Spiros

This is our first challenge. We have created it using the Genial.ly app. Our challenge is adressed to  Spain's groups 2 and 5. We hope you manage to solve it and that you enjoy it.

                                                                                                                Greece's group 4

This is our second challenge. We have created it using the Genial.ly app. This challenge is adressed to Spain's group 3. We hope you manage to solve it and that you enjoy it.

                                                                                                                 Greece's group 4

The solution to our first challenge is:

The correct answer is D. First of all we need to examine in which number the pattern ends. The total of the numbers written is 1+2+…+N= ½*N(N+1), N being the last number. So ½*N(N+1)= 105. Solving the equation, we will find out that N=14, rejecting the other solution which is N=-15. The final pattern is: 1,2,2,3,3,3,4,4,4,4,5,5,5,…,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14. The multipliers of 3 are 3,6,9,12 and their quantity in the pattern is 3+6+9+12=30.

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The solution to our second challenge is:

The correct answer is D. We can also look at the shape like two equal pyramids with a square base and height ½ (half of the cube’s height). The base of each pyramid is at a level that cuts out a square (the red line). Since the square base of each pyramid connects the middles of the red square, its area is half of the square’s. From the form of the pyramid’s volume each one has volume ½*base*height= 1/3*1/2*1/2= 1/12 so the initial shape’s volume is 2*1/12=1/6.