Yesterday’s post was inspired by Peter Norvig’s new year’s greeting, which was:
I thought his greeting was wonderful, but it bothered me that it relied so heavily on factorials, which many people don’t understand. I wondered whether it would be possible to use only add, subtract and multiply, plus concatenation (eg: 1 and 2 can become 12), so that more people would be able to read the message. For variety, I decided to put the digits in forward order.<\/p>\n
My strategy for finding a solution was to start with 2013 and work backwards, trying to whittle things down to zero. First I tried 2013 – 1234, but that gave 779, and I couldn’t see how to get from 779 down to zero using just the remaining digits 5,6,7,8,9.<\/p>\n
So I then backtracked and tried 2013 – 123. That gave me 1890, and I knew I was in luck, since 1890 is a multiple of 90, so it must also be a multiple of 45. That gave (2013 – 123) \/ 45 = 42, which is just 7 × 6 — two more digits down.<\/p>\n
At this point it was done, except for incorporating 8 and 9. Fortunately (8 – 9) is -1, which is easy to slip in, giving the final result: 0 + 123 – 45 \u00d7 6 \u00d7 7 \u00d7 (8 – 9) = 2013.<\/p>\n
Still, there was something very cool about the fact that Peter Norvig’s sequence was an actual countdown from 10 to 1 — just like the countdown to midnight at Times Square on New Years Eve. So this morning I figured I’d try such a countdown, again using only “easy to read” arithmetic.<\/p>\n
Since 2013 = 61 × 33, this time I took a different approach:<\/p>\n
33<\/big> →<\/big> 12<\/font> + 21 →<\/big> 4 × 3<\/font> + 21 Yesterday’s post was inspired by Peter Norvig’s new year’s greeting, which was: Happy 10\/9!*8!*7!-6!*5!\/4!+3!*2!+1! I thought his greeting was wonderful, but it bothered me that it relied so heavily on factorials, which many people don’t understand. I wondered whether it would be possible to use only add, subtract and multiply, plus concatenation (eg: 1 … Continue reading “(10 + 98 – 7 \u00d7 6 – 5) \u00d7 (4 \u00d7 3 + 21)”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/10861"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10861"}],"version-history":[{"count":137,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/10861\/revisions"}],"predecessor-version":[{"id":10997,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/10861\/revisions\/10997"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10861"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10861"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10861"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n<\/center>
\nAnd there you have it — the title of today’s post.<\/p>\n","protected":false},"excerpt":{"rendered":"