# Weekly Rompecabeza: How Many Miles to Rome? DSC members are among the smartest people in the world. But that doesn’t mean they can’t be smarter. With the help of our friends at American Mensa, DSC is proud to bring you weekly Rompecabezas (Spanish for “head breakers”) to boost your IQ into the Thermosphere.

Ever had a dream where you’re lost in a desert and you happen upon a signpost, and you’re all like, “Well, that make’s no sense, how can New York City and Los Angeles be that close? And why are all those cacti yellow?” Then you come-to and realize you hit your head on a tree branch earlier that day. The puzzle below is kind of like that. Need a hint? Here’s two:

Hint 1: The numbered miles have nothing to do with the actual distance. Duh!

Hint 2: The mileage has something to do with the words themselves.

Check back next week for the answer! Step 1: Substitute letter variables for the icons.

To start, focus on the first row across and first column down. Sub variables for the icons in both equations:

1) A + B + C + A = 205

2) A + B + B + B = 205

Step 2:  Solve the second equation for A.

A + B + B + B = 205

A + 3B = 205

A = 205 – 3B

Step 3: Go to the first equation (205), and substitute this new value of A (205 – 3B). Then solve for C.

A + B + C + A = 205

(205 – 3B) + B + C + (205 – 3B) = 205

410 – 5B + C = 205

C = 205 – 410 +5B

C = 5B  – 205

Step 4: Substitute letter variables for one of the 204 equations.

A + A + C + C = 204

2A + 2C = 204

Step 5: Now substitute your new values for A (205 – 3B) and C (5B – 205) into the equation for 204 (2A + 2C = 204), and solve for the single remaining variable, B.

2A + 2C = 204

2(205 – 3B) + 2(5B – 205) = 204

410 – 6B + 10B – 410 = 204

4B = 205

B = 51

Step 6: Plug this numerical value for B into the A + B + B + B = 205 equation to solve for A.

A + B + B + B = 205

A + 51 + 51 + 51 = 205

A = 52

Step 7: Plug the numerical values for A and B into your original equation to solve for C.

A + B + C + A = 205

52 + 51 + C + 52 = 205

155 + C = 205

C = 50

CONCLUSIONS

A = 52

B = 51

C = 50

Now that we know what each icon equals, we can solve for the missing number, 206.