math & puzzles Online Quiz - 170

This is possible. Amy's sister's grandmother is also Amy's grandmother. Her grandmother's son could be Amy's father or Amy's uncle. Therefore, the host (her uncle) could indeed be her sister's grandmother's son.

The sequence is based on adding consecutive integers: 10 (+5) -> 15 (+6) -> 21 (+7) -> 28. The next increment should be +8. 28 + 8 = 36. Therefore, the claim that he should give 35 is false.

For a rectangle to fit in a semi-circle of radius R, the distance from the center to the far corners must be <= R. Here, width is 6 (3 from center) and height is 3. Distance = sqrt(3^2 + 3^2) = sqrt(18) ≈ 4.24. Since 4.24 < 6, the picture fits easily. The statement is False.

A regular 12-sided polygon (dodecagon) can be divided into 12 equal triangles by drawing 6 diameters (straight lines passing through the center connecting opposite vertices). Each line splits the area, and 6 such lines create 12 equal sectors.

A wreath is a circular arrangement. In a linear arrangement of 8 pieces, you would need 7 or 9 ties depending on the method, but in a closed circle (wreath), the number of ties equals the number of pieces. Thus, 8 pieces require 8 ties.

By testing possibilities: If Ubuntu takes Tea, Suse and Fedora must take the same (Rule C). If they all take Tea, Rule B is satisfied (Fedora doesn't take coffee). If Suse takes Coffee, Fedora must match Ubuntu (Rule A). Suse is the only one whose choice remains consistent across valid logical constraints.

This is a prime number sequence: 2, 5, 11, 17, 23. These are consecutive prime numbers starting from 2. Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves.

The sequence consists of the cubes of consecutive odd integers: 1^3=1, 3^3=27, 5^3=125, 7^3=343. The next odd integer is 9, and 9^3 (999) equals 729.

The sequence follows the pattern n^2 + n (or n(n+1)): 1^2+1=2, 2^2+2=6, 3^2+3=12, 4^2+4=20, 5^2+5=30. The next term is 6^2+6, which is 36+6=42.

The sequence consists of the squares of descending integers: 9^2 (81), 8^2 (64), 7^2 (49), and 6^2 (36). The next number in the sequence is 5^2, which is 25.

The pattern is (Previous Term + 2) * 2 or simply adding 6, 12, 24... (doubling the difference). 2+6=8, 8+12=20, 20+24=44. The next difference is 48. 44+48=92.

The sequence consists of consecutive prime numbers in descending order: 97, 89 (skipped), 83, 79 (skipped), 73, 71 (skipped), 67. If following every second prime: 97, 83, 73, 67 are not strictly every second. However, 59 is the next prime after 61. 59 is the correct choice as it continues the descending prime sequence.

The sequence is squares of odd numbers: 1=1², 9=3², 25=5², 49=7². The pattern continues with the next odd number (9), giving 9²=81. Alternatively, each term is (2n-1)² where n=1,2,3,4,5.

The differences between the terms are increasing by one: 5-2=3, 9-5=4, 14-9=5. Following this pattern, the next difference should be 6. Adding 6 to 14 results in 20.

This sequence consists of every other prime number starting from 3: 3 (skip 5), 7 (skip 11), 13 (skip 17), 19 (skip 23), 29. The pattern selects alternate primes from the sequence 3, 5, 7, 11, 13, 17, 19, 23, 29...

The differences between consecutive terms are 11 (14-3), 22 (36-14), and 33 (69-36). Following this arithmetic progression of differences, the next difference should be 44. Adding 44 to 69 results in 113.

This is a classic logic puzzle, not a mathematical sequence. The first statement establishes that 1 equals 5, so by symmetry, if 1=5, then 5 must equal 1. While the pattern 5^1=5, 5^2=25, 5^3=125, 5^4=625 would mathematically lead to 5^5=3125, the riddle intends for you to recognize the reflexive relationship from the first statement.

This is a simple algebraic substitution problem. Given TCS=10, we can verify TCS+TCS=10+10=20, which matches the equation. Therefore, 5TCS=510=50. The question tests basic arithmetic and the ability to follow a given variable assignment through multiple operations.

To minimize time: 1 & 2 cross (2s), 1 returns (1s), 5 & 10 cross (10s), 2 returns (2s), 1 & 2 cross (2s). Total: 2+1+10+2+2 = 17 seconds. This strategy ensures the slowest people cross together to save time.

This is a word puzzle: he is writing an ICS exam sitting between two MATs. The word MATHEMATICS is formed by MAT + HEMAT + ICS. When you place ICS between two MATs, you get MAT-ICS-MATICS, which combined spells MATHEMATICS. The riddle uses the positioning of words to reveal the hidden term.