Charlie and Lynne 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
Can you find the values at the vertices when you know the values on
Can you coach your rowing eight to win?
A number of you commented on the fact
that the distribution we obtain from taking random samples may not
correspond to the actual distribution of the marbles. For example,
if a sample of 10 marbles does not contain a blue ball this does
not mean that there is no blue in the bag. Shanell from Garden
International School adopted the following strategy:
The important point is that the more
viewings we average over, the more likely we are to get the correct
distribution. This is a very important concept in probability -
it's worth giving it some thought if it doesn't make sense yet. A
good resource for seeing this phenomenon in action is
Bearing this in mind, can you suggest what
might be thequickest strategy for getting to 1000 points? You might
decide to take a fixed number of samples each round before
guessing. You'll have to decide what this fixed number is going to
be. Remember, the more samples you take each round the better your
chances of guessing correctly, but the more points you expend.
Maybe you could collect some data in a spreadsheet.