The object is to arrange three 9s to make 20. There is no trick involved. Simply arrange three 9s, using any standard arithmetic signs and symbols, to total 20. How can it be done?Ross solved this with help from the Internet. I know that will be disappointing for Mr. Shortz to learn, as he was so sure that this particular Sam Loyd puzzle wasn't on the Internet. It's not, but there is a website that shows you how you can create equations for all the numbers from 1 to 100 using only the numeral 4. Looking at the methods used on that site helped Ross to see what the trick here was:

9 + 9 / .9 = 20In other words, eighteen divided by nine-tenths equals twenty.

Mendo Jim is chortling somewhere, as we are currently using a very slo-o-ow satellite connection for the Internet and it's going to be a challenge to load sufficient photos on Flickr to actually mount a photos section. But I'm going to try. Here is November!

Time for:

0 - 25 26 - 50 51 - 75 76 - 100 - Joe Kupe 101 - 125 - Ross 126 - 150 151 - 175 - Curtis 176 - 200 - Magdalen 201 - 225 226 - 250 251 - 275 276 - 300 301 - 325 - Word Nerd 326 - 350 - Jay 351 - 375 - Maggie Strasser 376 - 400 401 - 425 - Fred 426 - 450 451 - 475 - Margaret G. 476 - 500 - David | 501 - 550 - B. Haven 551 - 600 - legolambda 601 - 650 651 - 700 701 - 750 751 - 800 801 - 850 851 - 900 901 - 950 - Sarah E. 951 - 1,000 1,001 - 1,050 - Natasha 1,051 - 1,100 1,101 - 1,150 1,151 - 1,200 1,201 - 1,250 1,251 - 1,300 1,301 - 1,350 1,351 - 1,400 1,401 - 1,450 1,451 - 1,500 | 1,501 - 1,550 1,551 - 1,600 1,601 - 1,650 1,651 - 1,700 1,701 - 1,750 1,751 - 1,800 1,801 - 1,850 1,851 - 1,900 1,901 - 1,950 1,951 - 2,000 2,001 - 2,250 2,251 - 2,500 2,501 - 2,750 2,751 - 3,000 3,001 - 3,500 3,501 - 4,000 4,001 - 4,500 4,501 - 5,000 More than 5,000 |

*In the event that a single round number is announced with a qualifier such as "about" or "around" (e.g., "We received around 1,200 entries."), the prize goes to the person who picked the range that includes that specific number.*

## 5 comments:

Too obvious for me. The only answer I thought of was too Hitchhikerish to have been what Sam Loyd intended.

Nice job, we got this too!

Nice answer though I still prefer (sqrt 9)!!/((sqrt 9)! (sqrt 9)!).

Of course there's also (Arccos (-9/9))/9, but some consider trig functions inelegant in this sort of puzzle, and besides that gives 20° not the unitless 20 as requested.

I'm going to be a stickler and say that your answer should be (9+9)/.9. Without the parentheses, order of operations dictates that you do 9/.9 before you add the first 9, making the answer 19.

Like Anon2:45, I also came up with (sqrt 9)!! / ((sqrt 9)! * (sqrt 9)!) = 3!! / (3! * 3!) = 720/36 = 20.

I wonder if there are any other answers?

Seth, awesome! We were playing around with factorials, roots and cubes and could not get it that way, nice job!

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