### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# The Moons of Vuvv

##### Stage: 2 Challenge Level:

"I enjoy your website", wrote Becky , from Carleton St Hilda's C. of E. Primary School. Becky sent her Vuvviaan moons solution to us in the form of a table. Becky's solution was one of three different suggestions for solutions to this problem sent in. The three relate to each other. See if you can find out how and why. Then have a look at the problem and see if you can decide which of the answers you agree with and why. This is how Becky began her solution search:

Now, I wonder what Becky changed her search to? If Becky is going to change her search to try and arrive at an answer perhaps she wants to think about this idea.

Alex and her family from Leicester, England worked on this Vuvvian problem. Alex explains how they set about arriving at a solution:

• We started off by doing the seven times table, because that was how long the last moon took to go round Vuvv.
• Next, we checked if the multiples of seven were also in the 2x, 3x, 4x, 5x, 6x tables. This was so we'd know if they (Vuvv moons) would line up.
• We got fed up working out the multiples of seven, because they got way too big. So, we used a calculator! We pressed +7=== to get the multiples of seven.
• We found out that it would take 210 Vuvvian years between each super eclipse.

Now although 210 years is a long time, Anita and Jing Jing from Kilvington Girls' Grammar in Australia, think that's only the half of it...in fact, they think that it is 420 year wait between Super-eclipses. But Thomas, from Suffolk, thinks it's way longer than that - twice as long.

He wrote: "There are 840 Vuvvianyears between the Super Eclipses. I worked it out by going through the 7 times table and writing it down seeing that this would be the hardest to divide by. I then realised that the number had to end in a zero because it had to be divisible by 5 and 2. That meant that all I had to do was find out if the multiples of 7 were divisible by 3, 4 and 6 and if they were multiply them by 10. In the end 84 was the lowest number divisible by 3, 4 and 6 so I multiplied it by 10 and got 840."

Franco and Jonny from Northamptonshire agree that is it 420. They say:

We started off with 42. Every number goes into 42, except 5, so we multiplied it by 5.

6 doesn't go into 210, so we went back to 42. We then multiplied 42 by 10, to get 420. We checked by dividing 420 by 1, 2, 3, 4, 5, 6 and 7. They are all factors of 420. So the overall answer is 420.

So, who is correct?