Number Sequences, Patterns, and Polygon Puzzles

You take the first pill at 0 minutes, the second at 30 minutes, and the third at 60 minutes. Therefore, the total time elapsed from the first to the last pill is 60 minutes. 90 minutes is a common distractor assuming 3 intervals of 30.

The rule is based on the number of letters in the month multiplied by 2. April (5 letters) = 10; May (3 letters) = 6 (though the prompt says 5, suggesting a different rule). If the rule is letters * 2.5: April (5*2.5=12.5) doesn't fit. If the rule is simply (Letters * 2.5) rounded, July (4 letters) would be 10.

The sequence follows an alternating pattern of adding 7 and 10: 3+7=10, 10+10=20, 20+7=27, 27+10=37, 37+7=44. Following this pattern, the next step is to add 10 to 44, resulting in 54.

An enneagon (also known as a nonagon) is a polygon with 9 sides. The name comes from the Greek 'ennea' for nine. An 8-sided polygon is an octagon.

An icosagon is a polygon with 20 sides. The name comes from the Greek 'eikosi' for twenty. Polygons with 30, 40, or 60 sides have different specific Greek-derived names.

A pentagon is a five-sided polygon. The prefix 'penta-' comes from the Greek word for five. A 6-sided polygon is a hexagon, and a 7-sided one is a heptagon.

A hendecagon (also known as an undecagon) is a polygon with 11 sides. The term comes from the Greek 'hendeka' meaning eleven. 12 sides is a dodecagon.

A heptadecagon is a polygon with 17 sides and 17 angles. The name is derived from 'hepta' (7) and 'deca' (10). 15 is a pentadecagon, and 16 is a hexadecagon.

A quadrilateral is a polygon with 4 sides (and 4 vertices/angles). Examples include squares, rectangles, and trapezoids. A 3-sided polygon is a triangle, and a 5-sided one is a pentagon.

In geometry, a chiliagon is a polygon with 1,000 sides. The prefix 'chilia-' comes from the Greek word for thousand. 100 is a hectogon, and 10,000 is a myriagon.

This is a product sequence where each term is the product of the previous two: 12=2, 22=4, 24=8, 48=32. Therefore, the missing number is 8.

The sequence follows the formula 2 * n^2: 2(1^2)=2, 2(2^2)=8, 2(3^2)=18, 2(4^2)=32, 2(5^2)=50, 2(6^2)=72. Thus, 50 is the missing number.

The pattern is (Previous + 1) * Multiplier: (1+1)*2=4, (4+2)*3=18, (18+3)*4=84, (84+4)*5=440. The next term is (440+5)*6 = 445 * 6 = 2670.

The differences between terms are: 11, 13, 15, 17, 19, 21. 1+11=12, 12+13=25, 25+15=40, 40+17=57, 57+19=76, 76+21=97. The sequence uses increasing odd numbers starting from 11.

The pattern follows: multiply by 2 and add consecutive odd numbers. 7 × 2 + 1 = 15, 15 × 2 + 3 = 33, 33 × 2 + 5 = 71, 71 × 2 + 7 = 149, 149 × 2 + 9 = 307. Each step doubles the previous number and adds the next odd number.

The pattern multiplies each number by an increasing integer: 3×2=6, 6×3=18, 18×4=72, so 72×5=360. Each step multiplies by 2, 3, 4, then 5.

The differences are 4, 14, 36. These are (3^1+1), (3^2+5)... no. Better: 13+2=5, 53+4=19, 193+18... no. Correct pattern: 1+(3^1+1)=5, 5+(3^2+5)=19, 19+(3^3+9)=55, 55+(3^4+13)=149. Wait, 119 is (55 + 64). Pattern is +4, +14, +36, +64? No, 119 is correct via 23^n-1 logic.

The pattern is (A-B) followed by (A+B). 7-6=1, 7+6=13 (113). 9-1=8, 9+1=10 (810). 5-3=2, 5+3=8 (28). For 7+2: 7-2=5 and 7+2=9, resulting in 59.