Mathematical Game--Cryptarithm

[Tom&Shelly]

Not sure if anyone here is interested in this sort of thing, but there is a type of mathematical game called a "cryptarithm". The idea is that each letter stands for a digit, each letter always represents the same digit, each digit is represented by a unique letter, and the goal is to find the digits represented by each letter that make the sum correct. Also, there are no leading zeros.

So here is one I came up with that seems appropriate here (there is one and--I believe--only one answer):

CAMPING
+ HIKING
=KICKASS

Note that the sum of two single digits can result in either a single digit, or a two digit number beginning with 1, so to solve these one has to consider the possibility of "carrying" a one. For example, from the one's digits, we have G + G equals either S or 10 + S. Then, either N + N equals S or 10 + S, or N + N + 1 = S or 10 + S.

Also note in this problem, CAMPING and KICKASS have seven digits, while HIKING has only six, and so A + H has to carry a one, therefore C + 1 = K.

Usually with these, one can write a number of equations like those above, eliminating many possibilities. Eventually, one then has to try the different possible combinations until one works. Or, these days, one can "cheat" and write a computer program to go through and try every combination "brute force".

So if you're into this sort of game, have fun! I'll post the answer in a day or two.

Tom

[tony.latham]

Tom:

Let me just throw my cards on the table.

Game + Mathematics is like Military + Intelligence.



I'm sitting here watching my CNC mill out a piece of aluminum. It's another learning-curve moment and the grade is steep. No math involved but a lotta fractions converted to millimeters so maybe so.

Tony

[Tom&Shelly]

Game + Mathematics is like Military + Intelligence.

Recreational math is definitely a different type of hobby.

I'm sitting here watching my CNC mill out a piece of aluminum. It's another learning-curve moment and the grade is steep. No math involved but a lotta fractions converted to millimeters so maybe so.

Tony

I'd certainly call converting fractions to mm math, Tony, and it solves a practical problem (engineering math--the best kind, says this retired engineer!)

I know you have that fraction calculator on your phone. Can that do the metric conversion as well? Or are you doing it some other way?

Tom

[tony.latham]

I know you have that fraction calculator on your phone. Can that do the metric conversion as well?

I've got another app for that. For damn sure. I haven't dreamed in millimeters yet but it may happen.

But... the aluminum milling came out great. Last night the bit galled up and made a mess. This single-flute bit did well.


Tony

[Tom&Shelly]

I've got another app for that. For damn sure. I haven't dreamed in millimeters yet but it may happen.

I wonder whether it would be possible to modify the CNC computer to take fractional inches? But that's a whole different hobby yet.

I was stationed in England in the late 1980's and it was curious to see how their transition to the metric system was going. We drove in miles per hour, but bought gasoline (on base, with ration coupons) in liters. The Brits bought theirs in imperial gallons. I bought a set of metric drill bits from the BX (because, like the gas, the BX/PX system was oriented towards troops in West Germany), but the British hardware stores only sold the same fractional inch drill bits we see in North America. The TV stations gave the temperatures in Celsius, but neither the Brits nor the Yanks understood that!

But... the aluminum milling came out great. Last night the bit galled up and made a mess. This single-flute bit did well.


Tony

Excellent!

[tony.latham]

I wonder whether it would be possible to modify the CNC computer to take fractional inches?

I do most of my 2D design work in Sketchup using inches. I export it as an SVG file and import it into software called EstlCam. That's where the millimeters start and I tell it how deep to cut. And of course, I'm using fractional bits. You start picking up on the fact that 3.18 mm is 1/8".

I was on a fire in the Yukon Territories about 1983. As we flew from Fairbanks, we were boning up on metric and I was going cross-eyed. When we got to Watson Lake for the briefing, Les, the old forester that was in charge answered our dilemma with this, "metric? We don't use that baloney here in the Yukon."

Worked for me.

Tony