Two squares overlap so that a vertex $A$ of the larger square, whose side is 25 cm, is at the centre of the smaller square, whose side is 24 cm. In the diagram $AB=13$ cm. Find the perimeter, in centimetres, of the shaded overlap quadrilateral. Enter the number only.
A rhombus has side length 17 and one diagonal of length 16. Find the length of its other diagonal. (The source's phrase “has a length of 17” is interpreted as side length, as in its solution.)
In a class of 50 students, 15 like Maths, 27 like English, and 13 like neither subject. How many like both Maths and English? Enter the number of students.
Jacob initially had 5 biscuits for every 3 that Sheila had. After Jacob gave Sheila 1 biscuit, he had 3 biscuits for every 2 that she had. How many biscuits did Jacob have at first?
A cricket climbs a staircase by jumping either 1 or 2 steps each time. In how many different ways can it climb an 8-step staircase? For example, a 3-step staircase has exactly three ways: $1+1+1$, $1+2$, and $2+1$. The order of jumps matters. Enter the number of ways.
Find the sum of the digits of the product $2017\times99999$.
Original printed choices: A. 201697983; B. 36; C. 201700000; D. 35; E. 10.
**Response format:** This self-study version uses numerical input. Enter the digit sum itself, not an option letter; the printed choices are retained for source comparison.
Continue the right-aligned rows shown: row $n$ contains $n$ consecutive positive integers in descending order, using every integer once. What number is directly below 526, in the same vertical column?
