SEAMO 2016 — Paper D — Grade 7–8

Mary climbs twelve stairs, taking one or two steps at a time. How many ways can she climb them?

A square’s side increases by $30\%$. By what percentage does its area increase?

A coin is tossed four times. Find the probability of exactly two heads.

Find $x$ in $2,9,-4,3,-10,-3,-16,x,-22,-15,\ldots$.

Primes $m,n$ satisfy $m+n=21$. Find the possible values of $(2n+1)/m$.

Find the sum of all negative factors of $105$.

Tae Kwon multiplies his birthday month by thirty-one and the day by twelve. The products sum to $265$. When is his birthday?

Evaluate $2015\times20162016-2016\times20152015$.

Evaluate $100^2-99^2+98^2-97^2+\cdots+2^2-1^2$.

How many digits are in $3\times4^{22}\times5^{45}$?

Today is Wednesday. What weekday is $20152015$ days later?

Bond leaves Follonica for Arezza at $8{:}00$ am at $150$ km/h, finishes his mission there within thirty minutes, then immediately returns at $100$ km/h, arriving at $11{:}00$ am. Find the distance.

Evaluate $1+2^1+2^2+\cdots+2^8$.

Fill the seven circles with $1,\ldots,7$ without repetition so that the three numbers on each of the three lines have equal sums. How many ways are there?

How many six-digit numbers $\overline{a8819b}$ are divisible by twelve?

A circle of circumference two metres rolls once around the outside of an equilateral triangle of perimeter six metres without slipping. How many turns does it make?

The clock shows $8{:}00$. How long until the minute hand next overlaps the hour hand?

There are nine white, five red and six black balloons. Select ten with at least two and at most eight white, at least two red, and at most three black. How many ways?

Candle A burns completely in three hours and candle B in five. B is shorter and thicker. Lit simultaneously, their remaining heights are equal after two hours. Find the initial height ratio A:B.

Find the largest $n$ such that exactly one whole number $k$ satisfies $\frac9{17}\lt \frac n{n+k}\lt \frac8{15}$.