Thursday, November 5, 2015

The Point is the Point

Here's this week's NPR Sunday Puzzle:
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 = 20 
In 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!

Ice Crystals In Morning Sunlight

--- Flowering Tree in November ---

~ ** The Last November Sunset 2012** ~

--- November Golden Reflection ---

~ Battle of the Windmill ~

Milad Tower / Tehran

Time for:
Here are this week's picks:
  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
Our tie-break rule:   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:

Henry BW said...

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

Joe Kupe said...

Nice job, we got this too!

Anonymous said...

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.

Seth said...

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?

Joe Kupe said...

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