### Where Can We Visit?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

### Gr8 Coach

Can you coach your rowing eight to win?

### Babylon Numbers

Can you make a hypothesis to explain these ancient numbers?

# In the Bag

##### Stage: 3 Challenge Level:
Ten marbles of varying colours are chosen at random and placed in a bag.
Can you guess the colours of the 10 marbles in the bag?

To help you make accurate predictions you can choose to see the results of 10 viewings - each viewing removes a marble out of the bag, records its colour and returns it to the bag before repeating the process.

You can choose to have as many viewings as you like before deciding to "Make a Guess".
Each Round concludes when you have made a guess.

If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.

Can you reach a score of 1000 points?

You start with 500 points. Each run of 10 viewings "costs" you 10 points but you can "earn" points by predicting accurately the contents of the bag:
150 points for a perfect match
100 points for 9 matching marbles
0 points for 8 matching marbles
-100 points for 7 or fewer matching marbles.

Can you develop an effective strategy for reaching 1000 points?
Can you develop an effective strategy for reaching 1000 points in the least number of rounds?