[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-632102-105":59,"doc-detail-632102-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","magic-square-5a-mathematical-puzzles-for-students","Magic Square 5A - Mathematical Puzzles for Students","","This educational document provides two magic square puzzles designed for 5th-grade students to enhance their arithmetic and logical reasoning skills. Each puzzle requires participants to arrange a specific set of numbers within a 3x3 grid such that the sum of every horizontal, vertical, and diagonal line equals a target value. The first challenge utilizes fractions and whole numbers to achieve a sum of 7.5, while the second employs decimals to reach a total of 1.5. Complete solutions for both puzzles are included, illustrating that multiple valid configurations exist through rotation or reflection, making this an ideal resource for math practice and self-assessment in classroom or home-learning environments.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/magic-square-5a-mathematical-puzzles-for-students/632102/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/magic-square-5a-mathematical-puzzles-for-students/632102.png","ImageObject",300,407,{"name":92,"@type":93},"Aria","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-10-22",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is a magic square?","Question",{"text":112,"@type":113},"A magic square is a grid where the sum of numbers in every horizontal, vertical, and diagonal line is equal.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the target sum for the first magic square puzzle?",{"text":117,"@type":113},"The target sum for the first puzzle using numbers 0 through 4.5 is 7.5.",{"name":119,"@type":110,"acceptedAnswer":120},"Are there multiple correct solutions for these puzzles?",{"text":121,"@type":113},"Yes, there are several solutions for each square, as different arrangements can be achieved through rotations or reflections of the base solution.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},632102,1792772655,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24},2336464648322,"https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488","MAGIC SQUARE 5A  \nA magic square is a square where each line of 3 numbers (vertical, horizontal and diagonal) adds up to the same amount.  \n1) Write the numbers 0, ½, 1, 1½, 2, 2½, 3, 3½, 4, 4½ in the correct place so that each line (vertical, horizontal and diagonal) adds up to 7½ .  \n½ 1 1½ 2 3 3½ 4 4½ Total must be 7½   \n2) Can you make a new magic square using the digits 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9 so that each line adds up to 1.5?  \n0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9  \nTotal must be 1.5   \n\n|  |  |  |\n| --- | --- | --- |\n|  | 2½ |  |\n|  |  |  |\n\n\n|  |  |  |\n| --- | --- | --- |\n|  | 0.5 |  |\n|  |  |  |\n\nMAGIC SQUARE 5A ANSWERS  \nPlease note that there are several solutions for each square puzzle. Each solution will be a reflection or a rotation of one of the solutions below.  \nOne solution for each challenge is given. 1)  \n½ 1 1½ 2 3 3½ 4 4½ Total must be 7½  \n\n| 2 | 1½ | 4 |\n| --- | --- | --- |\n| 4½ | 2½ | ½ |\n| 1 | 3½ | 3 |\n\n2)  \n0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 Total must be 1.5  \n\n| 0.2 | 0.9 | 0.4 |\n| --- | --- | --- |\n| 0.7 | 0.5 | 0.3 |\n| 0.6 | 0.1 | 0.8 |","cbCaikzZNheXoE3b","https://ap.wps.com/l/cbCaikzZNheXoE3b","pdf",175364,"English","# Magic Square Challenges\n## Puzzle 1: Fractions and Whole Numbers\n## Puzzle 2: Decimals\n# Answer Keys\n## Solution to Puzzle 1\n## Solution to Puzzle 2","[{\"question\":\"What is a magic square?\",\"answer\":\"A magic square is a grid where the sum of numbers in every horizontal, vertical, and diagonal line is equal.\"},{\"question\":\"What is the target sum for the first magic square puzzle?\",\"answer\":\"The target sum for the first puzzle using numbers 0 through 4.5 is 7.5.\"},{\"question\":\"Are there multiple correct solutions for these puzzles?\",\"answer\":\"Yes, there are several solutions for each square, as different arrangements can be achieved through rotations or reflections of the base solution.\"}]","Magic Square 5A - Mathematical Puzzles for Students | PDF",1792669934]