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A magic square is a square grid filled with distinct integers in such a way that the sums of the numbers in each row, each column, and both main diagonals are the same. This concept dates back thousands of years and can be found in various cultures around the world. One interesting variation of the magic square is called the "Magic Square Bumblebee." This type of magic square is characterized by a unique arrangement of numbers with a specific pattern resembling the body of a bumblebee. The distinctive design gives it its name. To create a magic square bumblebee, we start with a conventional magic square of odd order, such as 3x3, 5x5, or 7x7.

“It’s likely that significant ‘reforms’ will be instituted with the relaunch of Disneyland’s Annual Passholder program. Having the chance to reboot the entire program in the image of the Disney Flex Pass (which is essentially the framework for the Park Pass reservation system at Walt Disney World) should help address the crowd woes that have arisen at Disneyland in the last several years.” Nailed it? Nailed it.

Such benefits and discounts may not be combined with any other offer or promotion, are for personal use only, and may not be used for any commercial purpose or for the benefit of others including, without limitation, to obtain or purchase items or services with the intent to resell such items or services, or to share benefits with persons who are not the Magic Key holder. Next, there s the Enchant Magic Key, which seemingly replaces the Deluxe and Flex Passes the Flex itself seemed poised to phase out the Deluxe pre-closure.

To create a magic square bumblebee, we start with a conventional magic square of odd order, such as 3x3, 5x5, or 7x7. The numbers in the original magic square are then placed in a honeycomb pattern to form the shape of a bumblebee. The number in the center is typically the highest number, representing the head of the bumblebee.

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Magic Key discounts and benefits are dependent on pass type. To receive any applicable benefits or discounts, Magic Key holders must show their valid and activated Magic Key pass prior to purchases or offer redemptions. Further identification may be required. Benefits and discounts are valid at select Disneyland Resort owned-and-operated stores, restaurants and locations solely determined by Disney and are nontransferable, revocable and subject to exclusions, restrictions and change or cancellation without notice or liability. Such benefits and discounts may not be combined with any other offer or promotion, are for personal use only, and may not be used for any commercial purpose or for the benefit of others including, without limitation, to obtain or purchase items or services with the intent to resell such items or services, or to share benefits with persons who are not the Magic Key holder. From time to time, select third parties may also offer benefits and discounts to Magic Key holders and such offers shall be solely the responsibility of such third parties without any liability to Disney or its affiliates. Please ask about any applicable benefits and discounts at a location prior to purchase. Benefits and discounts are determined solely by Disney or the applicable location/store owner and are subject to restrictions and change or cancellation without notice or liability. Disney reserves the right to deny any benefits or discounts to any Magic Key holder at any time for any reason.

Magic Key merchandise discounts at select Disney owned-and-operated locations are not valid on certain items, including, without limitation: original or consignment art; select limited editions; select collectibles and specialty items (including, without limitation, one-of-a-kind art, Disney-branded original art, celebrity memorabilia, Savi's Workshop – Handbuilt Lightsabers, Droid Depot packages, framed Disney Dollars, framed Disney Gift Cards, framed ticket media, Artist Sketch Program (original art), Walt Disney Classics Collection, handmade products (physically touched by an artist or vendor), and artist-signed Vinylmation); cameras (digital, video, disposable and film); sundries; tobacco; alcohol; newspapers or periodicals; books; personalization; selection print packages and any online purchases from Disney PhotoPass service; outdoor vending (e.g., balloon vendors, glow vendors); postage stamps; rentals (e.g., strollers, ECV); pantry or prepared foods; kitchen products, electronics (MP3 players, video players, video games, CDs, DVDs, Blu-ray™ disks, videos and software media); treatments and cosmetics; Swarovski Crystal; national-branded fragrances, selected specialized toys, select product launches, select premium branded items, select reusable shopping bags, special orders; purchase-with-purchase offers; gift cards; gift certificates; park admission; ticket media; arcades; previous purchases; shipping or taxes, or on phone, email, online or mail order purchases. Dining discounts at select Disneyland Resort owned-and-operated restaurants and locations are not valid on alcoholic beverages, tobacco products, room service, holiday banquet buffets, select food and beverage novelty merchandise, previous purchases, taxes or gratuities. Restrictions and exclusions are subject to change without notice or liability. Please ask about any applicable benefits or discounts at an applicable location prior to purchase.

Magic Key holders must have both a theme park reservation and Magic Key pass valid for admission to the same park on the same date for park entry to access any store, restaurant or other location inside a theme park. Park reservations for Magic Key holders are limited in number and subject to the availability of park reservations allocated to Magic Key passes as determined by Disney, applicable Magic Key pass blockout dates, and theme park capacity. A Magic Key pass does not guarantee park entry, even on dates when a Magic Key pass is not blocked out. Magic Key holders, regardless of their Magic Key pass type, are not entitled to any or all reservations Disney makes available to others. Other restrictions apply, as set forth in the Magic Key Terms and Conditions, and may change from time to time in Disney’s discretion without notice or liability.

FPO: By clicking "Continue" you will be leaving Disneyland and will be redirected to Hong Kong website to purchase Hong Kong Disneyland Park Tickets from Hong Kong International Theme Parks Limited.

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The Disneyland Enchant Key annual pass has a more limited set of benefits all around. That pass offers:

The numbers are arranged in a way that maintains the sum equality in rows, columns, and diagonals. This unique arrangement provides an aesthetic touch to the conventional magic square. The magic square bumblebee not only showcases the mathematical concept of a magic square but also adds an element of creativity and visual appeal to it. It is an excellent example of how mathematical concepts can be transformed into visual art. The bumblebee pattern adds a fun and playful aspect to the traditional magic square, making it more engaging and captivating. Whether used for educational purposes or artistic expression, the magic square bumblebee serves as an excellent example of the versatility and aesthetic potential of mathematical concepts. It demonstrates how mathematics can be merged with creativity to create visually appealing patterns and designs. The bumblebee pattern, with its distinctive arrangement of numbers, adds a unique and memorable touch to the traditional magic square concept..

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