1. Snow Problem
Raymond gazed out his window and admired the snow-covered garden, where a perfect layer of 5 centimeters blanketed everything except the path. The snow was already beginning to melt.
The rectangular garden measures 16 meters on its longest side and 10.5 meters on the shorter side. The path is a narrow rectangle, 0.5 meters wide, leading from the street to the entrance.
Raymond started some rough calculations. We built a snowman made of three spheres, where the volume ratio of base, thorax, and head is 3:2:1.
His calculations use a simplified method which takes 4 times the cube of the radius for the sphere’s volume and overlooks snow compaction.
Based on this method, can you determine the radius of the snowman’s base sphere?
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2. Insulation Calculation
Sven Svendsen is almost ready for his North Pole expedition. An essential part of his preparation involves gaining weight for warmth.
Beginning today, he will start with his normal daily intake of 2,540 calories and will increase his calorie consumption by 100 calories each day over the next 20 days.
Sven plans to gain weight solely by consuming Wazoo multi-nutrient bars, each containing 140 calories.
How many days can he stick to this plan, only eating Wazoo bars?
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3. Advent Attempt
In December, a daily contest challenges players to guess a number between 1 and 10,000. A single lucky number will win a prize, remaining unchanged throughout the month. Incorrect guesses allow players to try again the next day.
In one household, Steve guesses daily, while his daughter Lottie has an advent calendar with 24 doors but doesn’t understand numbers yet. She can only open one door each day.
After Steve guesses three numbers and Lottie opens her three doors on December 3rd, who is more likely to have chosen correctly: Lottie with her doors or Steve with his numbers?
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4. PIN Puzzle
Janice, in a rush for Christmas shopping, was asked for her four-digit credit card PIN but struggles with memory.
Fortunately, she excels at solving mathematical problems and remembers the correct method to determine her PIN. She decisively calculates all unique three-digit numbers that sum to eight and contain no zeros.
These three digits together equal her four-digit PIN. Can you figure it out too?
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5. Word Play
- Rearrange the letters to form three scientific instruments: TER TEL ABE OMEAST OPE BAR ESC ROL
- Decode the names of three scientists: Zulksus, Chumnyeol, Ichimunichi
- Rearrange the letters to create three geometric shapes: GLE TRA REC IUM OID PEZ TAN IPS ELL
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6. Mysterious Gift
Zack forgot to label his Christmas presents. He recalls that silver gifts are not for his mother, and his father’s gifts are either gold or red.
The blue present is for his sister or brother. If his mother’s gift is red, then his sister receives the gold, and if his mother’s gift is gold, then his sister receives the blue gift. Who gets which present?
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7. Test the Metal
A chemist, physicist, and biologist were asked to complete a survey on their favorite metals. It turns out neither Ben nor the chemist likes tin, and biologists aren’t Kim, nor do they prefer iron. Gold is the favorite metal for both Mary and Kim. Can you uncover each scientist’s favorite metal?
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Answers
Snow Problem
Solved: 1 meter
Explanation: The garden’s area measures 168m² (10.5m x 16m). The path, being 0.5m wide and 16m long, occupies 8m². Thus, the snow-covered garden area is 160m². At a depth of 5 cm, the snow volume equals 160 x 0.05 = 8m³.
To find the snowman’s base volume, half of the snow (4m³) is used. The formula for a sphere’s volume leads to the equation 4r³ = 4m³, resulting in a base radius of 1 meter with a diameter of 2 meters.
Insulation Calculation
Solved: 3 days
Explanation: Begin by determining a target calorie value that divides evenly by 140. 2,940 is one such number (140 x 21). You can increase this by adding or decreasing 100 calories weekly. Thus, 2,240, 2,940, 3,640, and 4,340 are attainable calorie goals. By starting at 2,540 calories and incrementing daily over 20 days, you can reach 4,540 calories. The viable calorie values therefore yield three days of consuming only Wazoo bars.
Advent Attempt
Solved: It is more likely that Lottie opened the correct three doors in any order.
Explanation: Lottie opened three out of 24 doors on day one, two out of 23 on day two, and one out of 22 on day three. The probability of her correctly opening the doors multiplies, giving 6/12,144. Conversely, the chances of Steve guessing the lucky number are only 3/10,000. Therefore, Lottie has better odds of success.
PIN Puzzle
Solved: Janice’s PIN is 3552.
Explanation: To find a three-digit number, valid combinations must not include digits greater than 5. Acceptable pairs like (5,2,1) and (4,3,1) yield 6 permutations each. The sum of all configurations is calculated to determine her PIN as 3552.
Word Play
- Telescope, Barometer, Astrolabe
- Faraday, Pasteur, Einstein (using letter shifting techniques)
- Ellipsoid, Rectangle, Trapezoid
Mysterious Gift
Solved: His mother receives the gold gift, his father gets the red, his sister has the blue, and his brother receives the silver.
Test the Metal
Solved: Ben—Physicist—Iron; Mary—Biologist—Tin; Kim—Chemist—Gold.
Read more:
- Top 10 Coldest Places on Earth
Source: www.sciencefocus.com
