Problem Statement

There are 7 chairs in a row, numbered 1 to 7. Seven people, also labelled 1 to 7, must sit in these chairs, one person per chair. Person i is allowed to sit only in chair i - 1, i, or i+1 (where chair 0 and chair 8 do not exist, so person 1 can use only chair 1 or 2, person 7 only chair 6 or 7, etc.). In how many seating arrangements can all 7 people be seated while respecting these constraints? 21 14 18 24 How many liters of water must be added to 20 liters of a 40% sugar solution to make it a 25% sugar solution? 20 liters 12 liters 15 liters 10 liters Find the value of the 30th term of the series below: (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 The average age of 5 teammates is 14 years. If one of them is 11 years old, what is the total age of the remaining four teammates? 68 years 54 years 59 years 48 years The Line chart shows the