answer:Offering unique and exotic microgreens can be a great way to differentiate your product and attract restaurants looking to add something new and exciting to their menus. Here are some unusual microgreens that might pique the interest of chefs: 1. Shungiku (Chrysanthemum greens): A popular ingredient in Japanese cuisine, shungiku microgreens have a delicate, slightly bitter flavor and a beautiful, lacy texture. 2. Purslane: This succulent microgreen has a tangy, slightly sour taste and a crunchy texture, making it a great addition to salads, sandwiches, and seafood dishes. 3. Sorrel: With its bright, citrusy flavor and delicate texture, sorrel microgreens are perfect for adding a burst of freshness to soups, salads, and sauces. 4. Radish greens (Daikon or Watermelon radish): These spicy, peppery microgreens are great for adding a kick to salads, sandwiches, and Asian-inspired dishes. 5. Cress (Garden or Watercress): Peppery and refreshing, cress microgreens are perfect for adding depth to salads, soups, and sauces. 6. Amaranth: This ancient grain's microgreens have a slightly sweet, nutty flavor and a beautiful, fuchsia-colored hue, making them a great garnish for salads and cocktails. 7. Mustard greens (Red or Green): With their pungent, slightly spicy flavor, mustard microgreens are great for adding a tangy kick to salads, sandwiches, and Indian-inspired dishes. 8. Tatsoi (Bok choy): These delicate, Asian-style microgreens have a mild, slightly sweet flavor and a beautiful, rosette-shaped appearance, making them perfect for adding a pop of color to salads and stir-fries. 9. Chervil: This French herb's microgreens have a delicate, anise-like flavor and a beautiful, lacy texture, making them perfect for adding a subtle, sophisticated touch to salads, soups, and sauces. 10. Wasabi greens: For those who like a little heat, wasabi microgreens have a spicy, pungent flavor and a beautiful, heart-shaped appearance, making them a great addition to sushi, sashimi, and other Japanese-inspired dishes. Consider experimenting with different blends of microgreens to create unique flavor profiles that can add an extra layer of complexity to dishes. Some examples include: * A spicy mix featuring radish, mustard, and wasabi microgreens * A French blend with chervil, sorrel, and arugula microgreens * An Asian-inspired mix with shungiku, tatsoi, and purslane microgreens What type of restaurants are you targeting with your microgreens, and do you have any specific chefs or culinary styles in mind that you'd like to cater to?

answer:To solve this problem, we first identify the positive integers less than 20 that are divisible by 3. These integers are 3, 6, 9, 12, 15, and 18. We can pair each of these integers with the remaining integers less than 20 to check which pairs satisfy the given conditions. Since one integer in the pair must not be divisible by 3 and their sum must be greater than 12, we can consider the possible pairs for each of the integers divisible by 3. For 3, the possible pairings that meet the sum condition are with integers from 10 to 19, but we have to exclude 12, 15, and 18 since they are divisible by 3. This leaves 7 possible pairs for 3: (3,10), (3,11), (3,13), (3,14), (3,16), (3,17), and (3,19). For 6, we similarly exclude integers less than 7 and integers divisible by 3, leading to the pairs (6,7), (6,8), (6,10), (6,11), (6,13), (6,14), (6,16), (6,17), and (6,19). For 9, we exclude integers less than 4 and those divisible by 3, giving the pairs (9,4), (9,5), (9,7), (9,8), (9,10), (9,11), (9,13), (9,14), (9,16), (9,17), and (9,19). For 12, the pairs would be (12,1), (12,2), (12,4), (12,5), (12,7), (12,8), (12,10), (12,11), (12,13), (12,14), (12,16), (12,17), and (12,19). For 15, the possible pairings are (15,1), (15,2), (15,4), (15,5), (15,7), (15,8), (15,10), (15,11), (15,13), (15,14), (15,16), (15,17), and (15,19). For 18, the pairs are (18,1), (18,2), (18,4), (18,5), (18,7), (18,8), (18,10), (18,11), (18,13), (18,14), (18,16), (18,17), and (18,19). However, we have double-counted some pairs, such as (3,16) and (15,4), since 3 + 16 and 15 + 4 are essentially the same type of pair but reversed. Considering this, we can reorganize our counting approach. Instead, we can count the number of integers that can pair with 3, 6, and 9. The rest will be the same as the pairings with 12, 15, and 18, but reversed. For 3, 6, and 9, we have 7 + 9 + 11 = 27 pairings. For the remaining numbers 12, 15, and 18, their possible pairings are already included in the 27 counts, so we don't add more. However, we have counted (3,10) but not (10,3). For each pair of integers divisible by 3, we counted only one side of the pairing. So, the numbers 7, 8, 10, 11, 13, 14, 16, 17, and 19 (which can pair with 3, 6, and 9) can also be the first number in the pair, not just the second. By considering this, the numbers 4 and 5 can pair with 9, 12, 15, and 18; and 1 and 2 can pair with 12, 15, and 18, but not 3, 6, or 9 because the sum will be less than or equal to 12. Therefore, they do not need to be added again. Considering these reversals, 1, 2, 4, and 5 have pairings with 12, 15, and 18 that haven't been counted yet. 1 and 2 can pair with 12, 15, and 18, giving 6 additional pairs. 4 and 5 can pair with 12, 15, and 18 as well, but they were counted in 9's pairings, so we only need to add 4 and 5's pairings with 12, 15, giving

answer:There are indeed 37 distinct pairs of positive integers less than 20, where one integer is divisible by 3 and the other is not, and their sum is greater than 12. This result correctly counts both the original pairings and their reversals, without double-counting any pairs.

answer:Poncelet's Porism is a beautiful result in geometry, discovered by French mathematician Jean-Victor Poncelet in 1813. It is a theorem in projective geometry, which is a branch of mathematics that deals with geometric properties preserved under projections. The statement of Poncelet's Porism is as follows: consider two conics (e.g., ellipses, circles, parabolas, or hyperbolas) in the plane. Suppose we have an n-sided polygon that is inscribed in the outer conic and circumscribed around the inner conic, meaning its vertices lie on the outer conic and its sides are tangent to the inner conic. Poncelet's Porism states that if there exists one such n-sided polygon, then there are infinitely many such n-sided polygons, all of which have the same n sides. In simpler terms, if you can find a polygon with n sides that fits snugly between two conics, with its vertices on the outer conic and its sides tangent to the inner conic, then there are infinitely many such polygons with the same number of sides. This result is often referred to as a porism, which is an old Greek term for a mathematical proposition that establishes the possibility of a geometric construction without actually performing it. Poncelet's Porism has far-reaching implications in geometry and has been influential in the development of projective geometry. It also has connections to other areas of mathematics, such as algebraic geometry and dynamical systems. The result has been generalized and extended in various ways, but the underlying idea remains a beautiful example of the deep connections and symmetries that exist in geometric mathematics.