Transcript EPSY 602
EPSY 602 Problems Fall 2004 Cryptarithmetic Problem Problem BEST + MADE MASER Treat this as an addition problem. Change letters to numbers such that constraints represented in the problem are satisfied. The 8 different letters that can take on any value from 0 to 9, but no letter can assume more than one value. Solution July 18, 2015 Copyright © 2004 - Robert J. Hall 2 Algebra Word Problem A candle factory has two workers, Jones and Smith. Jones makes candles at the rate of 60 per hour and Smith makes 75 candles per hour. Jones spends one hour more than Smith each day making candles. If Jones makes the same number of candles each day as Smith, how long does Smith work? Solution July 18, 2015 Copyright © 2004 - Robert J. Hall 3 Word Puzzles MOMANON PRICE EGAMI AMY TERTHENET 33 CO. MAKE MNN NOBODY’S THE LAW Solution July 18, 2015 Copyright © 2004 - Robert J. Hall 4 Summary Using specific operators and observing constraints, the problem solver moves from an initial state to a goal state. In well-defined problems, the initial state and the goal are explicit from the onset. In ill-defined problems; the problem solver must first identify the states. Knowledge-lean problems require relatively little domain knowledge. Knowledge-rich problems require much domain knowledge. July 18, 2015 Copyright © 2004 - Robert J. Hall 5 Cryptarithmetic Problem B EST + MADE MASER 1 1 1 9567 + 1085 10652 • The first letter to be assigned a number would be ‘M.’ ‘M’ can only be the result of a carry and therefore must equal 1. • With ‘M’ equal to 1, ‘B’ would have to equal 8 or 9 to effect the carry. If ‘B’ equals 8 or 9, then ‘A’ equals 0. • With ‘A’ equal to 0, we know that ‘S’ equals ‘E’ + 1 (carried from the 10s column. We also know that ‘S’ + ‘D’ equals ‘E’ which means that ‘D’ would have to equal 8 or 9 depending on the number assigned to ‘B’ and that if ‘D’ equals 8 there must be a carry from the 1s column. • ‘B’ has to be 9 because if ‘B’ equals 8 then ‘D’ would have to equal 9 then the ‘E’ + ‘A’ (0) = ‘S’ would not result in the carry that would be necessary for the 1000s column. • ‘B’ then equals 9, ‘D’ equals 8, ‘E’ equals 5, and ‘S’ equals 6. That leaves ‘T’ and ‘R’. From the remaining numbers, ‘T’ would have to equal 7 and ‘R’ 2.With Return July 18, 2015 Copyright © 2004 - Robert J. Hall 6 Algebra Word Problem A candle factory has two workers, Jones and Smith. Jones makes candles at the rate of 60 per hour and Smith makes 75 candles per hour. Jones spends one hour more than Smith each day making candles. If Jones makes the same number of candles each day as Smith, how long does Smith work? Let t = length of time Smith works t + 1 = length of time Jones works The length of time Smith works times 75, then, would equal the number of candles that Smith produces and the length of time Jones works times 60 would equal the number of candles that Jones produces. To produce the same number of 60 (t + 1) = 75t 60 = 15t candles per day Smith would work 4 hours and Jones would have to 60t + 60 = 75t 4=t work 5 hours. Return July 18, 2015 Copyright © 2004 - Robert J. Hall 7 Word Puzzles Frame Games MOMANON PRICE MAN IN THE MOON HALF PRICE AMY EGAMI REVERSE IMAGE BIGAMY TERTHENET 33 CO. THREE’S COMPANY THE INTERNET NOBODY’S THE LAW MAKE MNN MAKE AMENDS Return July 18, 2015 NOBODY’S ABOVE THE LAW Copyright © 2004 - Robert J. Hall 8