2008 xIMC keystage2-EMIC individual

Starting at the central circle, move between tangent circles. How many paths cover four circles containing $2,0,0,8$, in that order?

Three ducks and two ducklings weigh $32$ kg. Four ducks and three ducklings weigh $44$ kg. Ducks have equal weights, as do ducklings. Find the weight of two ducks and one duckling.

If $25\%$ of sitting people stand and $25\%$ of standing people sit, $70\%$ are then standing. What percentage were initially standing?

A $3$ m sedan at $110$ km/h overtakes a $17$ m truck at $100$ km/h. Find the time from the sedan front reaching the truck rear to its rear reaching the truck front.

Arrange all six-digit numbers using each digit $0,1,2,3,4,5$ exactly once in ascending order. Find the $502$nd.

How many seven-digit numbers use only $2$ and $3$, with no adjacent $3$s?

The six-digit number $\overline{abcabc}$ has exactly $16$ positive divisors. Find its smallest value.

How many five-digit multiples of $3$ have at least one digit equal to $3$?

Parallelogram $ABCD$ has area $60$ cm$^2$. Points $M$ on $AD$, $N$ on $AB$ satisfy $AM=2MD$, $AN=2NB$. Lines $BM,DN$ meet at $O$. Find the sum of the areas of $BON$ and $DOM$.

The four-digit number $\overline{ACCC}$ is $\frac25$ of $\overline{CCCB}$. Find $ABC$, the product of the digits.

Square $ABCD$ has side $4$ cm. $E,F$ are midpoints of $AD,BC$. A radius-$4$ arc centred at $C$ meets $EF$ at $G$; a radius-$2$ arc centred at $F$ meets it at $H$. The difference between the areas bounded by $GH,BG,BH$ and by $EG,DE,DG$ is $(m\pi-n)$ cm$^2$. Find $m+n$.

In a chess tournament boys number twice the girls. Every pair plays once, with no draws. Girls win games and boys win games in ratio $7:5$. How many boys participate?

In the pictured addition, each different symbol denotes a different digit. Three equal five-digit numbers are added. Find the five-digit result.

Positive integers fill the grid in the arrow order shown. For example $8$ is in row $2$, column $3$, and $9$ in row $3$, column $2$. Which row and column contain $2008$?

A 24-hour clock displays $\mathrm{HH:MM:SS}$, from $00:00:00$ to $23:59:59$. How many times are the first three digits identical, in order, to the last three? Example: $13:21:32$.