{"id":57559,"date":"2022-06-24T18:09:08","date_gmt":"2022-06-24T16:09:08","guid":{"rendered":"https:\/\/www.studiogiochi.com\/2022\/06\/mental-calculation-fixed-missing-138\/"},"modified":"2022-07-20T17:02:46","modified_gmt":"2022-07-20T15:02:46","slug":"mental-calculation-fixed-missing-138","status":"publish","type":"post","link":"https:\/\/studiogiochi.com\/en\/2022\/06\/mental-calculation-fixed-missing-138\/","title":{"rendered":"Mental Calculation: fixed missing “138”"},"content":{"rendered":"
[vc_row][vc_column width=”1\/4″ el_class=”download”][vc_single_image image=”30538″ img_size=”full”][\/vc_column][vc_column width=”3\/4″][vc_column_text]\n

THE GREAT BOOK OF FAST AND MENTAL CALCULATION:<\/h2>\n

Fixed the missing “138” in the “Seven 7” problem<\/i><\/h2>\n[\/vc_column_text][vc_column_text]\n

The challenge was to get all the numbers from 1 to 150 using 7 seven times as well as the necessary arithmetic symbols.
\nIn the Great Book of Fast and Mental Calculation<\/strong><\/em><\/a>, Dario De Toffoli and Furio Honsell had proposed all the solutions\u2026 except one. The 138 had in fact remained unsolved, as far as we know no one had managed to reach it with the conditions posed by the problem.
\nBut now an old friend has succeeded, Silvano Berton, who has made it with the triangular numbers. But after all, if the factorial holds, why shouldn’t the triangular hold?
\nDon Knuth, computer guru, had for example already proposed to call the n-th triangular numbers “terminals”, indicating them with “n?”)… and Furio Honsell validated the solution.<\/p>\n

7? = 28 (the 7th triangular seventh)
\n(7+7)? = 105 (the 14th triangular) therefore:
\n7? + (7+7)? + 7 – (7+7)\/7 = 28 + 105 +7 -2 = 138[\/vc_column_text][vc_row_inner][vc_column_inner width=”1\/6″][\/vc_column_inner][vc_column_inner width=”4\/6″][vc_single_image image=”56922″ img_size=”full” add_caption=”yes” alignment=”center”][\/vc_column_inner][vc_column_inner width=”1\/6″][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row]\n<\/div>","protected":false},"excerpt":{"rendered":"

24 June 2022: thanks to our old friend Silvano Berton, he finally has a solution to the problem of the “Seven 7” that had remained unsolved in the Great Book of quick and mental calculation<\/em>: to obtain the number “138” using seven times the 7 and the necessary mathematical symbols.<\/p>\n","protected":false},"author":9,"featured_media":56929,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[509],"tags":[],"class_list":["post-57559","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-interventions"],"yoast_head":"\nMental Calculation: fixed missing "138" - studiogiochi<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studiogiochi.com\/en\/2022\/06\/mental-calculation-fixed-missing-138\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mental Calculation: fixed missing "138" - 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