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Math Logic Senior Division

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Hint: Look at the powers of each base number: \(x^1\), \(x^2\), \(x^3\).

Solution: In row 1: \(3^1=3, 3^2=9, 3^3=27\). In row 2: \(4^1=4, 4^2=16, 4^3=64\). Therefore, for row 3: \(5^1=5, 5^2=25, 5^3=125\). Correct answer is 125.

Lateral Thinking High School Classic

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Hint: Lighting a rope from both ends burns it twice as fast, taking exactly 30 minutes!

Step-by-Step Solution:
1. Light Rope 1 at both ends, and simultaneously light Rope 2 at one end.
2. Exactly 30 minutes later, Rope 1 burns out completely. At this moment, exactly 30 minutes of Rope 2 is left.
3. Immediately light the other end of Rope 2. The remaining 30 minutes will burn out in exactly 15 minutes!
4. Total elapsed time = 30 + 15 = 45 minutes.

Code & Cipher All Classes

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Hint: O is 15th, W is 23rd, and L is 12th in the alphabet.

Solution: O = 15, W = 23, L = 12. Sum = \(15 + 23 + 12 = 50\). The correct value is 50!

Junior Explorer Class 1 to 6

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Hint: The wolf doesn't eat cabbage. Only the goat causes problems when left with either!

Solution: The farmer must take the Goat across first, leaving the wolf alone with the cabbage (wolves don't eat cabbage). Then return, bring the cabbage, and bring the goat back, and so on!

Geometry & Angles Olympiad Challenge

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Hint: In 15 minutes, the hour hand has moved forward a quarter of the way toward 4!

Solution: The minute hand is pointing exactly at 3 (90° from 12). The hour hand moves at 0.5° per minute. In 15 minutes, it moves \(15 \times 0.5° = 7.5°\) past 3. Therefore, the angle between them is exactly 7.5°.

Mental Math Class 1 to 6

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Hint: If all 10 animals were chickens, there would be \(10 \times 2 = 20\) legs. The extra 8 legs must belong to the cows!

Solution: Extra legs = \(28 - 20 = 8\). Each cow has 2 extra legs compared to a chicken. Therefore, number of cows = \(8 \div 2 = 4\) cows (and 6 chickens). \(4 \times 4 + 6 \times 2 = 16 + 12 = 28\) legs!