math & puzzles Online Quiz - 65

The number of trailing zeros in n! equals the number of times 10 appears as a factor, which is limited by the number of 5s. For 15! we count multiples of 5: 5, 10, 15 gives three 5s, and 25 would contribute another but 25 > 15. Thus there are exactly 3 trailing zeros.

This sequence follows the pattern where each term after the first two is the product of the previous two terms divided by a decreasing integer. The terms 0, 1, 1, 1, 2, 2, 3, 6 follow the pattern T(n) = T(n-2) × T(n-1) / k where k decreases. The next term is 3 × 6 / 4 = 4.5, and the subsequent is 6 × 4.5 / 1 = 27, giving approximately 4, 24.

For uniformly accelerated motion, velocity varies with the square root of distance traveled. Using v^2 = u^2 + 2as, if AP:PB = 1:5, then P is at 1/6 of the total distance from A. Solving gives v_P^2 = v_A^2 + (1/6)(v_B^2 - v_A^2), yielding v_P = 6 m/s. This is a standard kinematics relationship.

The series follows the pattern n^2 - 1: (1^2-1)=0, (2^2-1)=3, (3^2-1)=8, (4^2-1)=15. The next two terms are (5^2-1)=24 and (6^2-1)=35.

The series increases by successive even numbers: 3+4=7, 7+6=13, 13+8=21, 21+10=31. The next increment should be 12, so 31+12=43.

The number of trailing zeros in n! is determined by the number of factors of 5. In 12!, the multiples of 5 are 5 and 10. Each contributes one factor of 5. Since there are plenty of even numbers to provide factors of 2, there are 2 zeros.

The logic uses the reverse alphabetical position (Z=1, Y=2... A=26). Z(1) + P(11) = 12. Therefore, A(26) + K(16) = 42. Distractors are wrong because they use standard alphabetical order or incorrect math.

In this classic logic puzzle with one truth-teller and one liar, asking 'Which door would the other guard say leads to hell?' forces both guards to point to the same door - the door leading to heaven. The truth-teller truthfully reports what the liar would say (the liar would falsely claim hell leads to heaven), while the liar lies about what the truth-teller would say. Both end up identifying the heaven door.

This is a duplicate of question 92321 - the classic two guards logic puzzle. The optimal question is 'Which door would the other guard say leads to hell?' because it forces both the truth-teller and liar to point to the same door. The liar lies about what the truth-teller would say, while the truth-teller truthfully reports what the liar would say - both identify the heaven door.

In this logical system, sane humans always tell the truth (sane + believes true things), and insane vampires always lie but believe false things (insane + believes false things + vampire nature means lying). Therefore, statements from sane humans (truth about truth) or insane vampires (lying about falsehood) always result in true statements. The other combinations can produce false outputs.

This Hindi riddle describes three birds in a straight line: one bird at the front (has two behind), one bird at the back (has two in front), and one bird in the middle (has one in front and one behind). The translation preserves the riddle's logic about relative positions. Three is the only number that satisfies all conditions simultaneously.

Work backwards: the devotee has 2 flowers after the 4th door. Before door 4: (2+1)*2 = 6. Before door 3: (6+1)*2 = 14. Before door 2: (14+1)*2 = 30. Before door 1: (30+1)*2 = 62. Verification: 62→31 (31 taken), 31→15.5→16 (16 taken), 16→8 (8 taken), 8→4 (4 taken), 4→2 (2 taken) leaves 2.

The pattern follows prime number positions in the alphabet: B(2), C(3), E(5), G(7), K(11), M(13), Q(17). Each letter's position is a prime number. Option A (Q=17) fits, while W(23), S(19), and R(18) don't maintain the sequential prime pattern.