### Gambling at Monte Carlo

A man went to Monte Carlo to try and make his fortune. Whilst he was there he had an opportunity to bet on the outcome of rolling dice. He was offered the same odds for each of the following outcomes: At least 1 six with 6 dice. At least 2 sixes with 12 dice. At least 3 sixes with 18 dice.

### Marbles and Bags

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

### Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

# Jewellery Boxes

##### Stage: 4 Short Challenge Level:

Suppose that initially the total value of the jewels in $P$ is $£A$, and those in $Q$ is $£B$.

The average value in $P$ at the start is $\frac A3$. After the jewel has been moved it is $\frac{A-5000}2$. Therefore:

\frac A3 = \frac{A-5000}2 - 1000

Multiplying by $6$ and collecting like terms gives $A = 21000$.

The average value in $Q$ at the start is $\frac B3$. After the jewel has been moved, the average value is $\frac{B+5000}4$. Therefore:

\frac B3 = \frac{B+5000}4 - 1000

Multiplying by $12$ and collecting like terms gives $B = 3000$.

Therefore the total value is $£24,000$

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem