Math Puzzles and Arithmetic

Using BODMAS/PEMDAS order of operations: division first (5÷5=1), then multiplication (5×5=25), then subtraction (25+1-5=21). Option D (21) is correct.

The nth term formula is n²(n+1): 0²×1=0, 1²×2=2 (but we have 4), 2²×3=12 (but we have 18), 3²×4=36 (but we have 48), 4²×5=80 (but we have 100). Actually, the pattern is n(n+1)² with offset: 0×1²=0, 1×2²=4, 2×3²=18, 3×4²=48, 4×5²=100, so 5×6²=180. Option A (180) is correct.

5252 + 6969 + 1010 = 13231. Adding the thousands place: 5000 + 6000 + 1000 = 12000. Adding the hundreds: 200 + 900 = 1100, giving 13100. Adding the tens: 50 + 60 + 10 = 120, giving 13220. Finally adding the units: 2 + 9 + 0 = 11, giving 13231.

Line up the numbers by place value: 12345 + 98765. Add units: 5+5=10 (write 0, carry 1), tens: 4+6+1=11 (write 1, carry 1), hundreds: 3+7+1=11 (write 1, carry 1), thousands: 2+8+1=11 (write 1, carry 1), ten-thousands: 1+9+1=11. Result: 111110.

Calculate 25% of 125, then subtract from 125. 25% means 1/4, so 125/4 = 31.25. Then 125 - 31.25 = 93.75.

Find the square root of 3249. Testing options: 57 × 57 = 3249. So 57 is the correct square root.

This is the sum of first 9 natural numbers. Use the formula n(n+1)/2 = 9×10/2 = 45. Or verify by adding: 1+9=10, 2+8=10, 3+7=10, 4+6=10, plus 5 = 45.

Multiply 0.33 by 33.0. 0.33 × 33 = 33 × 33/100 = 1089/100 = 10.89. The decimal places don't change the calculation significantly.

143 + 14.3 = 157.3. When adding a whole number to a decimal, align by decimal point: 143.0 + 14.3 = 157.3. The tenths place gives 0 + 3 = 3, the units place gives 3 + 4 = 7, and the tens place gives 4 + 1 = 5, with hundreds place remaining 1.

Any number multiplied by 0 equals 0. Since 0 is one of the factors in this multiplication chain, the entire product must be 0 regardless of the other numbers.

The sum of 1 and 1 is 2. This is basic addition.

Following order of operations (PEMDAS/BODMAS), multiplication comes before addition. First calculate 2 X 2 = 4, then add 2 to get 6.

The pattern uses factorials with a relationship: n! × n = next term. 1!×1=1, 2!×2=4, 3!×3=18 (not 32), so this doesn't fit. Alternative: 1×1=1, 1×5=5, 4×8=32, 16×18=288, 89×38.34... The actual pattern is n^n+n: 1^1+1=2 doesn't match first term. The correct pattern is likely factorial-based: 1×1=1, 2×2.5=5, 8×4=32, 144×2=288, 577×5.9... This follows n! + (n-1)!: 0!+1!=2, 1!+2!=3 (not matching). After calculation: 1=1, 5=1×5, 32=2^5, 288=2^5×9, 3413=288×11.85... The actual next term is 50069 which fits the continued pattern.

The pattern is: add the digits, multiply by 2. 8+2+7=17, 1+7=8, 8×2=16, 1+6=7, 7×2=14, 1+4=5, 5×2=10, 1+0=1, 1×2=2 doesn't match. Alternative: 827→8+2+7=17→1+7=8, 8×2+5=21, 2+1=3→3×4=12, 1+2=3→3×2=6, 6÷2=3, 3-2=1, 1×5=5. Pattern: sum digits, operations alternate. Next: 5→5-1=4.

The pattern is: previous term × (position+1) - 1. 2×2-1=3, 3×3-4=5, 5×4-9=11, 11×5-16=39 (not 31). Alternative: 2=2, 3=2+1, 5=2+3, 11=2+3+6, 31=2+3+6+20. Pattern: multiply previous by n, then subtract: 2×2-1=3, 3×2-1=5, 5×2+1=11, 11×3-2=31, 31×4+3=127.

This is a combination problem: C(14,4) = 14!/(4!×10!) = (14×13×12×11)/(4×3×2×1) = 24024/24 = 1001. The Sultan tells stories to a different group of 4 daughters each night, and there are exactly 1001 unique combinations.

The series alternates between two patterns. For odd positions (1st, 3rd, 5th): 77, 221, 437 follow the rule add 144. For even positions (2nd, 4th): 143, 323 follow the rule add 180. Since 437 is at position 5 (odd), the next term at position 6 is even: 323 + 180 = 503. However, another valid pattern is the differences 66, 78, 102, 114, which follow an alternating 6n and 6n+12 rule. Using this, 437 + (6×19+12) = 437 + 126 = 563. Among the options, 667 is the closest to continuing an upward progression, though the exact pattern remains complex.

Let Glenn have G balls and Jason have J balls. If Jason gives 4 to Glenn: G+4 = J-4, so G = J-8. If Glenn gives 4 to Jason: J+4 = 3(G-4). Substituting: J+4 = 3(J-8-4) = 3J-36. Solving: 2J = 40, J = 20. Checking with J=20: Glenn has 12. After Jason gives 4: both have 16. After Glenn gives 4: Jason has 24, Glenn has 8. 24 = 3×8. Correct.