Find the next term of the following sequence:
2, 12, 1112, 3112, 132112, ...
**Editorial note for this self-study exercise:** For this self-study exercise, use the source’s look-and-say rule: describe each consecutive run of equal digits in the previous term, from left to right. Enter the next term as a number.
A container is filled with water to a height of 12cm. A stone of volume 585cm³ is dropped into it. Find the new height of the water if the tank has a square base of 15cm length.
**Editorial note for this self-study exercise:** Assume a tank with vertical sides and internal base side 15 cm; the stone becomes fully submerged, no water spills or is absorbed, and there is enough room for the new level. Enter the height in centimeters.
Nick is counting the sheep in a flock as they cross a road. The sheep begin to cross the road at 2 : 00 p.m. and cross at a constant rate of three sheep per minute. After counting 42 sheep, Nick falls asleep. He wakes up an hour and a half later, at which point exactly half of the total flock has crossed the road since 2:00 p.m. How many sheep are there in the entire flock?
A. 630
B. 621
C. 582
D. 624
E. None of the above
**Editorial note for this self-study exercise:** Enter the number of sheep, rather than an option letter.
The figure below shows a margin of 4cm from 2 sides of a rectangle PQRS. Given that PQ = 2PS and the area of the shaded region is 116 cm², find the perimeter (in cm) of the rectangle PTVU.
In the figure below, ABCD is a rectangle, the point E is the midpoint of AD and F is the midpoint of CE. If the area of rectangle ABCD is 96cm², find the area of triangle BDF.
70% of the pupils in a hall were boys. When 108 boys had left the hall, the number of girls was three times the number of boys remaining in the hall. Find the original of pupils in the hall.
**Editorial note for this self-study exercise:** Only the stated 108 boys leave; no girls leave and nobody enters. The last sentence asks for the original number of pupils.
Town E and Town F were 240km apart. Jason left Town E at 9.00a.m traveling at an average speed of 60km/h. Karen left Town E some time later than Jason and overtook him at 11.00a.m. Karen’s traveling speed was 90km/h.
a) At what time did Karen leave Town E?
b) How long had Karen rested when Jason finally reached Town F?
**Editorial note for this self-study exercise:** Assume both travel along the same route toward F at the stated constant speeds, without stops before F; Karen rests at F immediately after arriving. Enter part (a) as HH:MM on a 24-hour clock, then part (b) as a number of minutes, separated by a semicolon, with no spaces in the answer.
There were 640 coins in Bottle P, 865 coins in Bottle Q and 1260 coins in Bottle R. Sally transferred some coins from bottles Q and R into Bottle P. The ratio of the number of coins in Bottle P to the total number of coins in bottles Q and R became 5 : 2. How many coins were transferred into Bottle P?
A seven-digit number, $2\,006\,\square\square\square$, is divisible by 3, by 4 and by 25. Find the possible values of the missing digits.
**Editorial note for this self-study exercise:** Enter all possible three-digit endings in increasing order, separated by semicolons, with no spaces in the answer; give the missing blocks, not the full seven-digit numbers.
