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K Sengupta
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Solve this cryptarithm, where each of the letters represent a different decimal digit from 0 to 9. None of T and E is zero, and “EVENLY” is even.
(THINE)/(EVENLY) = 2/15
(THINE)/(EVENLY) = 2/15
jimmysnyder said:I have been finding these by writing and running a program that runs through all the possible values of the digits and prints out the ones that satisfy the defining equation. As such, they are not very interesting. Is there any method to these puzzles other than brute force that I am missing? In other words, is there any brain teasing going on here?
Can such plugging away actually solve the problem or simply reduce the time (nearly zero) that the inevitable program takes to run?davee123 said:There's some-- for instance, we know that (THINE) must be divisible by 2, and that (EVENLY) must be divisible by both 5 and 3. Hence, Y must be 0 or 5, and E must be one of 0, 2, 4, 6, 8. Next, you can rule out 8 as a possibility for E, because the maximum value for (THINE) is 98764, which means (EVENLY) has a max of 740730, meaning that E cannot be greater than 7. Next, we can rule out T=1, because the minimum value of (EVENLY) is 101235, which would make (THINE) be 13498. Since E =/= T, T clearly can't be 1.
Anyway, you can plug away at these bit by bit in that fashion, but yeah, it's certainly easy to write a brute force program to do the job.
DaveE
jimmysnyder said:Can such plugging away actually solve the problem or simply reduce the time (nearly zero) that the inevitable program takes to run?
"Thine/ evenly = 2/15" is a mathematical equation that represents a ratio or proportion. It can also be read as "Thine is to evenly as 2 is to 15".
The numbers 2 and 15 represent the quantities of the two variables being compared in the ratio. In this case, "Thine" and "evenly" have a ratio of 2 to 15.
This equation can be used in various ways in scientific studies, such as calculating proportions in experiments or analyzing data sets. It can also be used in chemistry to determine the molar ratio of elements in a compound.
Yes, the values on either side of the equation can be interchanged as long as the ratio remains the same. For example, "evenly/ Thine = 15/2" would still represent the same ratio of 2 to 15.
The equation "Thine/ evenly = 2/15" can be written as a fraction, decimal, or percentage without changing its meaning. For example, it can be written as "Thine is 2/15 of evenly", "Thine is 0.1333... times evenly", or "Thine is 13.33...% of evenly".