A friend passed this on to me on Tuesday. I’m sure the Fido Puzzle shows some type of mathematical formula in action. If I was a math teacher, I’m sure I’d know what it is and I’d put my students to work figuring it out as quickly as possible. Is this an Algebra thing? Trig? I haven’t a clue, but I’m curious. The Fido Puzzle asks first for either a 3- or 4-digit non-repeating number (1234), second for another number using the same digits as the first number (4321), third for the sum of those two numbers subtracted (3087), and fourth for all but one of those digits to be mixed into another number (730, leaving out the 8). By typing in 730, the Fido Puzzle will tell me that the number I’ve left out is 8, almost like the puzzle is reading my mind. Math teachers, let me know what you think of this.

#### Sell It

Intrigue the kids by showing them the puzzle online a few times, letting kids call out the answers to the different steps. “There’s got to be a pattern here. This Web site is certainly not reading our minds. There has to be a way this is working. Everything is a system based on rules. Let’s run a bunch of numbers through this thing and see if we can find the pattern that explain how this works. Then you can play this on your friends and surprise even that one that has that really cool card trick you can never do.” Or something to that effect. Modify as appropriate.

#### Gather

Students work in groups of two, spawning roughly 15 groups in your classroom. 7 of your groups will create 3-digit numbers and the rest will create 4-digit numbers. Using a worksheet you put together ahead of time (not my best work, but it’s a start), students catalog the different numbers that they generate through each step of the puzzle. Students keep track of their original number, the number they created, the resulting sum of the subtraction, the number they circled, and their final mixed up number.

#### Examine

Looking at the relationship between columns D and E holds the key, I’m convinced (for instance, if the numbers in column E add up to 10, column D is 8; if E adds up to 11, D is 7). And if your entire class can compile their results, that’s a lot of data to examine. Do this all day, examine the data the next, and you’ll have more than you’ll need to find a pattern.

#### Tell Me

Math teachers, can you use this? Is this a silly parlor trick that holds no educational value? Does this graph out in some predictable way? Can this serve as a segue or introduction to some other concept that’s useful? If nothing else, can you use it to show students how to solve a problem by gathering data and examining the data for trends?

### 3 comments

3. Grade 3 Brainbusters » Blog Archive » Fido Puzzler Can’t Read Our Minds! says:

[…] While browsing blogs last week, Mrs. Turner came across this post from Thoughts on Teaching: ” I’m sure the Fido Puzzle shows some type of mathematical formula in action. If I was a math teacher, I’m sure I’d know what it is and I’d put my students to work figuring it out as quickly as possible…” […]

1. Cassyt says:

[10/19/2007 - 8:26 am]

My third grade students have taken on your challenge and found the mathematical pattern behind the Fido puzzle. We used your worksheet, although with one change: in column C, you subtract the smaller number from the larger. One cannot assume that column A will always contain the larger number (minuend) and the puzzle does not take negative numbers into consideration. My class thanks you for the challenge and an engaging night of home enjoyment!