day/dydd 131 at 7puzzleblog.com

T he Main Challenge

Can you insert the numbers 0 to 9 exactly TWICE each into the gaps below so all five lines work out arithmetically?

◯  +  ◯   =    15    =   ◯  +  ◯
◯  +  ◯   =     5     =   ◯  –  ◯
◯  +  ◯   =    10    =   ◯  ×  ◯
◯  –  ◯   =     2     =   ◯  ÷  ◯
◯  +  ◯   =     9     =   ◯  ×  ◯

If you enjoyed attempting this, click this Mathelona link for details of our slightly easier pocket book challenges.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 3rd & 6th rows contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

What is the sum of the numbers in the 40’s?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are FIVE ways of making 131 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 131 by inserting 4, 5, 7 and 9 into the gaps on each line?

•  ◯×◯×◯–◯ = 131
•  ◯×◯×√◯+◯ = 131
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://7puzzleblog.com/131/", "fetch_time": 1652798696000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2022-21/segments/1652662517485.8/warc/CC-MAIN-20220517130706-20220517160706-00630.warc.gz", "warc_record_offset": 1043603, "warc_record_length": 8156, "token_count": 550, "char_count": 1410, "score": 3.9375, "int_score": 4, "crawl": "CC-MAIN-2022-21", "snapshot_type": "latest", "language": "en", "language_score": 0.4959909915924072, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00060-of-00064.parquet"}