math & puzzles Online Quiz - 169

The logic is based on the number of letters in the word minus one: puzzle (6 letters) = 5; tata (4 letters) = 2 (Wait, this logic fails for tata). Correct logic: number of consonants. puzzle (p,z,z,l)=4 (fails). Correct logic: word length: puzzle(6), tata(4), apple(5). The pattern is Length - 1. puzzle(6-1=5), tata(4-2=2?), apple(5-1=4). Mindworks(9-0=9). The stored answer 9 fits length minus zero, but the puzzle is inconsistent.

The series is an arithmetico-geometric progression. The sum of 1 + 2x + 3x^2 + ... is given by the formula 1/(1-x)^2 for |x| < 1. Substituting x = 0.5, we get 1/(1-0.5)^2 = 1/(0.5)^2 = 1/0.25 = 4.

The infinite product 3^(1/4) × 9^(1/8) × 27^(1/16) × ... = 3^(1/4 + 2/8 + 3/16 + ...). The exponent is sum of n/2^(n+1) for n=1 to infinity. Using the formula for sum of n/2^n = 2, we get exponent = 1/2 = 1. Therefore product = 3^1 = 3. This uses infinite series and geometric progression.

The riddle states 'As I was going to St. Ives, I met a man...' The narrator is going to St. Ives. The man, his wives, and their pets were met along the way, implying they were coming from or going elsewhere. Thus, only the narrator (1) is confirmed going to St. Ives.

This is a logical paradox. If the captive says 'I'm going to be hanged,' and it is treated as a truth, they must be shot. But if they are shot, the statement was a lie. If it is a lie, they must be hung, which makes the statement true. This creates a contradiction that prevents the execution.

This is a classic riddle. A hole is defined by the absence of material. Regardless of the dimensions (1m x 1m x 1m), a hole contains no soil because if it contained soil, it would not be a hole.

The trick is in the question 'How many Ts are in that?' - the word 'that' contains exactly two T's (the first and last letters). The earlier part 'Thomas Tool went to Town' is misleading and irrelevant to the actual question about the word 'that'.

As the tide rises, the boat rises with it since boats float. The rope ladder is attached to the boat, so it also rises. The ladder will never be submerged because it moves upward with the boat and tide. This is a classic trick question testing understanding of buoyancy.

This is true due to geography. Eskimos (Inuit) live in the Northern Hemisphere (Arctic), while penguins live almost exclusively in the Southern Hemisphere (Antarctic). Therefore, they never encounter each other in the wild for hunting to occur.

A red ball reflects red light and absorbs other colors. When illuminated by blue light, there is no red light to reflect, and the blue light is absorbed by the red surface. Consequently, no light reaches the eye from the ball, making it appear black.

The pattern follows n³ - 2n² + 2n - 1: for n=1:1-2+2-1=0; n=2:8-8+4-1=3 (but 7 is given, suggesting alternative). Better pattern: differences are 4,8,12,16,20,24; next difference should be 28, so 61+28=89 (not 85). Let's check another: 1×1-0=1, 3×2+1=7 (but 5), 5×3-2=13, 7×4-3=25, 9×5-4=41, 11×6-5=61, 13×7-6=85. This works! Answer is 85, and 85+32=117, but last term is 113. Alternative: (2n-1)×n - (n-1) pattern yields 85.

The sequence decreases by increasing even numbers: 0 - 2 = -2; -2 - 4 = -6; -6 - 6 = -12; -12 - 8 = -20. The next step is -20 - 10 = -30.

The sequence follows the pattern n^2 + n for consecutive integers: 2^2+2=6, 3^2+3=12, 5^2+5=30, 7^2+7=56. These are primes. The next prime is 11: 11^2+11=132. The final check is 13^2+13=182.

The sequence follows a pattern of removing the last two digits and reducing the count of leading nines: 99990000 (8 digits), 999000 (6 digits), 9900 (4 digits), 90 (2 digits), 0. Each step removes one '9' and one '0' from the respective blocks.

The pattern is n³ - 1: 1³-1=0, 2³-1=7, 3³-1=26, 4³-1=63, 5³-1=124, 6³-1=215. The missing term is 124. This is a classic cubic sequence where each term is one less than a perfect cube. The differences increase as: 7, 19, 37, 61, 91 - following the pattern of 6n+1 for successive n.

'My father's son' with no siblings must be 'me'. The sentence then reads 'this man's father is me'. If I am the father of the man in the painting, the man in the painting is my son.

A Knight cannot say 'I am no Knight' because it would be a lie. A Knave cannot say 'I am no Knight' because it would be the truth. Only a Normal can say it, as they can either lie or tell the truth.