Wolfram|Alpha's ability to handle numbers is well known, as you may have seen in past posts. But did you know it can also handle English words and letters, too?

In today's post, we'll take a look at the possibilities of solving puzzles with Wolfram|Alpha, by pitting it against some word and number puzzles from our old friend mental_floss.

First up, let's see what Wolfram|Alpha can do against word ladders. Here's one challenging you to change the word CARD to the word FLIP. You can't just ask it to solve the puzzle, but it can help you understand the possibilities.

One of the best strategies is to work inwards from both the top and bottom words, in order to see which words get closer to each other.

Start by entering _ARD into Wolfram|Alpha. You get the words BARD, CARD, DARD, GARD, HARD, LARD, SARD, WARD, and YARD back in response. CARD is the word we're starting with, so that can be eliminated. Dard and Gard are proper nouns, and uncommon, so you can probably eliminate those as possibilities, as well.

Continuing this procedure with C_RD, CA_D, and CAR_, we build up a good list of words to start off with: BARD, HARD, LARD, SARD, WARD, YARD, CORD, CURD, CARE, CARK, CARP, CARS, and CART. Trying the same approach with _LIP, F_IP, FL_P, and FLI_, we build up a list of these words: BLIP, CLIP, SLIP, FLAP, FLOP, and FLIT.

Comparing both lists, CARP and CLIP seem promising candidates, as they begin and end with C and P. Let's ask Wolfram|Alpha about C__P. Eliminating CARP and CLIP themselves, we wind up with the list: CAMP, CHAP, CHIP, CHOP, CLAP, CLOP, COMP, COOP, CORP, COUP, CROP, and CUSP.

The big trick with changing CARP to CLIP seems to be the switching of the vowels and the consonants, so COOP will obviously be a big help here. To get from CARP to COOP, we could use CORP, and to get from COOP to CLIP, we could use CLOP, so that seems to do it! Let's take a look at the word ladder we developed:

CARD

CARP

CORP

COOP

CLOP

CLIP

FLIP

Taking a peek at the answer, we see that we arrived at a different answer, but in the same number of steps!

There are even some word puzzles to which Wolfram|Alpha is extremely well-suited. One such mental_floss quiz involved naming all the non-obscure words of 4 letters or more made from the letters of the word SIXTEEN. Simply give Wolfram|Alpha the command word subsets sixteen, and after it generates the list, sort it by length. After removing any words shorter than 4 letters, proper nouns, and words that could reasonably be considered obscure, you get the words: EXIST, EXITS, INSET, NIXES, STEIN, TEENS, TENSE, TINES, EXIT, NEST, NETS, NEXT, NITS, SEEN, SENT, SINE, SITE, SNIT, TEEN, TEES, TENS, TIES, TINE, and TINS - 24 words in a quiz where 16 is considered a win!

Occasionally, mental_floss offers puzzles with the question “What number comes next in this sequence?”, such as this one. There's a slight problem with these, in that you can set up a formula for any set of numbers.

Let's say I decide that I want 137 to be the next number in the sequence in the puzzle above. I simply set up 9 equations so that each number in the sequence will create a 0 at some point, as follows: (x-1)(x-2)(x-2)(x-4)(x-8)(x-12)(x-96)(x-108)(x-137). When x = 108, you're multiplying by (108 - 108), so you're effectively multiplying everything else by 0.

That equation expanded becomes x^{9} - 370x^{8} + 48509x^{7} - 2636704x^{6} + 53341412x^{5} - 488919184x^{4} + 2206290496x^{3} - 5008709376x^{2} + 5422344192x - 2181758976. So, you can state that 137 is the next number in that sequence, because it's the next point that, when plotted, crosses the axis at 0 in our formula.

Remember, I just made up the number 137, so it could be any other number just as well. Perhaps you prefer 512? 42? 675? You can find an appropriate formula that will work for any of them. The answers to mental_floss' number sequence puzzles are rarely mathematical in nature. However, our example puzzle happens to be an exception.

Have you solved any mental_floss puzzles by using Wolfram|Alpha to help, or even cheat? I'd love to hear about it in the comments!

## Wolfram|Alpha vs. mental_floss

Published on Thursday, May 24, 2012 in fun, math, puzzles, software

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