Problem Statement

Seven chairs stand in a row, numbered 1 to 7, and seven people, also labelled 1 to 7, must each take one chair. Person i is only allowed to sit in chair i - 1, i, or i+1 (chair 0 and chair 8 don't exist, so person 1 can only use chair 1 or 2, person 7 only chair 6 or 7, and so on). How many valid seating arrangements satisfy this rule for all 7 people? 21 14 18 24 How many liters of plain water need to be mixed into 20 liters of a 40% sugar solution to bring it down to a 25% sugar solution? 20 liters 12 liters 15 liters 10 liters Work out the 30th term of this series: (1) + (2 + 3) + (4 + 5 + 6) + (7 + 8 + 9 + 10) +... N terms. 12412 17236 12321 13515 Let N = 2^7 * 3^4 * 5^2. How many invertible residue classes x (mod N) satisfy x^8 ≡ 1 (mod N)? 128 96 64 192 Five teammates average 14 years of age. If one of them is 11 years old, what do the remaining four add up to in total age? 68 years 54 years 59 years 48 years A line chart shows the ratio of Exports to Imports for two ship manufac