math & puzzles Online Quiz - 48

Robert and Scott each say 'One of the other two stole it. I did not do it.' Tommy says the same thing but we know he's lying. If Tommy is lying, then his statement 'One of the other two stole it AND I did not do it' is false. This means it's NOT the case that someone else stole it while Tommy is innocent. Since there's only one thief, this implies Tommy himself is the thief. If Tommy stole it, then Robert and Scott are telling the truth when they say 'I did not do it' (they didn't) and 'one of the other two' (Tommy) stole it.

Pattern: $(a \times b)$, $(a \times c)$, then $a \times (b+c)$. For $5+9+4$: $5 \times 9 = 45$, $5 \times 4 = 20$, and $5 \times (9-1)=40$ or similar concatenation. The result 452040 follows the $(a \times b)(a \times c)(a \times [b+c-1])$ logic.

The logic follows: $(a \times b) + (a \times c)$ and other digit manipulations. For $5+9+2$: $5 \times 9 = 45$, $5 \times 2 = 10$. The pattern across examples suggests the result 144400 through specific multiplication and subtraction of the terms.

Pattern: $(a \times b)$, $(a \times c)$, then $a \times (b+c)$ reversed or similar. Specifically: $6 \times 7 = 42$, $7 \times 9 = 63$, and the last part is derived from the sum/difference logic. $6+7+9$ gives 426327 based on the established concatenation of products.

By placing the individuals in a circle according to the constraints (C-A together, E-H opposite, G-D spacing), the relative positions are fixed. Following the clockwise/counter-clockwise logic of the seating, E ends up two places to the right of B.

The task is to arrange the numbers based on the magnitude of the words: Hundred (4), Thousand (2), Million (5), Billion (3), Trillion (1). This sequence (4 2 5 3 1) orders them from smallest to largest value.

This is a classic lateral thinking riddle. 'All but nine died' means that only nine sheep survived. Therefore, the shepherd is left with exactly 9 sheep. The other numbers (0, 8, 17) result from misinterpreting the phrasing.

The dial of a telephone contains the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. The product of any set of numbers that includes zero is always zero. Since zero is not listed in the specific numeric options, 'None of these' is correct.

The number of handshakes among $n$ people is given by the combination formula $n(n-1)/2$. For 10 people: $10 \times 9 / 2 = 45$. Each person shakes hands with every other person exactly once.

The digit 3 appears in the units place 10 times (3, 13, 23...93) and in the tens place 10 times (30, 31, 32...39). Total occurrences: $10 + 10 = 20$. Note that 33 counts twice (once for each place), which is included in this count.

Let $x$ be the number of correct sums. The number of wrong sums is $2x$. Total sums: $x + 2x = 48 \Rightarrow 3x = 48 \Rightarrow x = 16$. Thus, the student solved 16 sums correctly and 32 incorrectly.

$9 + 98 + 9 = 116$. Checking the options: $348 / 3 = 116$. $345 / 3 = 115$. Since $116$ is the sum, $348/3$ is the correct mathematical representation.

Digits: 1-9 (9 digits), 10-99 (90 numbers $\times$ 2 = 180 digits), 100-366 (267 numbers $\times$ 3 = 801 digits). Total: $9 + 180 + 801 = 990$. Option 1098 is incorrect as it assumes all 366 pages have 3 digits.

A square has 4 sides. If each side has 27 poles, the 4 corners are shared between two sides. The formula is $4n - 4$, where $n$ is the poles per side. $4(27) - 4 = 108 - 4 = 104$. Simply calculating $27 \times 4 = 108$ double-counts the corners.

This is a geometric progression where $a=1$ and $r=2$. The income on day $n$ is $ar^{n-1}$. For the 10th day: $1 \times 2^{(10-1)} = 2^9 = 512$. Option 1024 is incorrect as it represents the 11th day ($2^{10}$).

The code shifts each letter back by 2 positions in the alphabet: $M-2=K, I-2=G, N-2=L, D-2=B$. Applying this to DIAGRAM: $D-2=B, I-2=G, A-2=Y, G-2=E, R-2=P, A-2=Y, M-2=K$. This results in BGYEPYK.

The relationship is $x \rightarrow (x^2 / 2)$. For 8: $(8^2)/2 = 64/2 = 32$. Applying this to 10: $(10^2)/2 = 100/2 = 50$.