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Text File | 1992-06-13 | 90.4 KB | 32 lines

"The key to problem solving is in using what could be termed `whole-brain' thinking──the logic and rigor of the left brain, combined with the free-form visual and metaphorical thinking of the right." "If you're like most of us, at the first opportunity you'll fall into the old habit of assuming that your first definition of a problem is the correct definition. No problem. But the first time you realize that an inaccurate problem definition has cost you several weeks work or several hundred thousand dollars, or has given you a bad feeling about your problem solving ability...please remember the alternate route." "In a computer, all things and actions of the real world must be represented by words, numbers, images, or sounds." "It is the ability to recognize patterns, and the situations that invoke them, that separates the expert from the novice. Normally, this ability is developed as a result of random experience and takes a great deal of time to develop. It is possible, however, to speed up the process. The trick is to consciously learn those patterns and the kinds of situations they are associated with." "Complex problems are almost never solved by going directly from HERE to THERE. They're solved by inching forward, correcting, erasing, and rethinking. Problem solving is a PROCESS, and no one has ever shown you the process──until now." ├ └ ≡ └ └ ⁿⁿ≡ ⁿ? ⁿⁿ? └? ≡ └ ⁿⁿ≡ ≡ⁿ ≡ ⁿ? └? └ ⁿ └ ⁿⁿ≡ ⁿⁿ ⁿ └ⁿ └ └ ⁿ ├ ⁿⁿ≡? ⁿ ⁿ └ⁿ ?└ ├ⁿⁿⁿ≡?└ ⁿ≡ⁿ ≡ⁿ ?└ └ ├ⁿⁿⁿ≡?└ ⁿ≡ⁿ ⁿⁿ ?└ ?≡ ├ⁿⁿⁿ≡?└ⁿ≡ⁿ≤ ⁿ ?└ ?≡ ├ⁿⁿⁿ≡?└ⁿ≡ⁿ≤ ⁿ ?└ ⁿ ├ⁿⁿⁿ≡ ≡ⁿ≡ⁿ≡ └ⁿ ?└ ├ⁿⁿⁿ≡ ⁿⁿ≡ⁿ≡?≡ⁿ ?└ └ ├ⁿⁿⁿ≡ ⁿⁿ≡ⁿ≡ⁿⁿ ?└ ?└ ├ⁿⁿⁿ≡ ⁿ≡ⁿ≡ⁿⁿ ?└ ≡ ├ⁿⁿⁿ≡ ⁿ≡ⁿ≡ ⁿ ?└ ⁿ ├ⁿⁿⁿ≡ ⁿ≡ⁿ≡ ╧ⁿ ?└ ├ⁿⁿⁿ≡?└ ⁿ≡ⁿ≡? ⁿ ?└ ├ⁿⁿⁿ≡?└ ⁿ≡ⁿ≡ ⁿ ?└ ? ├ⁿⁿⁿ≡?└ ⁿ≡ⁿ≡ ⁿ? └? └ └ └ ⁿ ⁿ≡ ⁿ? └? └ └ └ ⁿⁿ ⁿ≡ ⁿ? └? └ ≡ⁿ ≡≡?ⁿ └ ≡ └ ⁿ └ⁿ? ≡ⁿ@╚ ⁿⁿⁿ ╧ └ ⁿ0 ╧ ⁿ ╧ ⁿ╠≡ⁿ≡≡ⁿ ≡?╧ ⁿⁿⁿⁿⁿ╧╧ ╧ ⁿⁿⁿ╧╧╧ ⁿⁿⁿⁿⁿ╧╧ ╧ ⁿⁿⁿ╧╧╧ ⁿⁿ≡<ⁿ≡ ╧ ⁿ ≡? ╧ ≤╧╧ ≤?╧ ⁿ?╧ ╧ ╧ ≤╧╧ ≤╧╧ ≤╧╧ ≤╧╧ ⁿ?╧ ╧ ⁿ╧ ≡╧╧ ≡╧╧ ≡╧╧ ?╧ ╧ ⁿ?╧ ≤╧╧ ≤╧╧ ≤╧╧ ╧ ╧ ╧ ≤╧╧ ≤╧╧ ≤╧╧ ⁿ?╧ ╧ ⁿ ╧ ≡╧╧ ≡╧╧ ≡╧╧ ⁿ?╧ ╧ ⁿ ╧ ≡╧╧ ≡╧╧ ≡╧╧ ⁿ?╧ ╧ ? ╧ ? ╧ < ╧ < ╧ ╧ ╧ ╧ ╧ ≡ └ └ └ ≡ ⁿ? ≡?<? ≡ ⁿ? ⁿ ╧ⁿ? ├ ≡ ⁿUUUUUUUUUUUUUUUUP ╧ⁿ ├ ≡ ⁿUUUUUUUUUUUUUUUUP ╧0ⁿ?├ ≤ ≤ ⁿⁿ ⁿUUUUUUUUUUUUUUUUP └0 ╧ ⁿ? ≤ ⁿ ⁿ ⁿUUUUUUUUUUUUUUUUP ≡? ⁿ ≤ ⁿ ⁿ ⁿUUUUUUUUUUUUUUUUP ├ ≡<ⁿ ≤ ⁿ ⁿ ⁿUUUUUUUUUUUUUUUUP ├ ╠≡<<? ≤ └ⁿ└ ⁿUUUUUUUUUUUUUUUUP ├ ??≤└ⁿ0?? ├ ╧╧≡ ≡ ⁿUU@UUUUUUUUUUUUP ⁿ ├ⁿ<?≤≡ⁿ<ⁿ ├ └≡ ≡ ⁿUUTUUUUUUUUUUUUUP ⁿ<?├≡≤?╧ⁿ≡≤ ├ ├ ≡ ≡ ⁿUUTUPTQEEE@UUPⁿ ≡├ⁿ └└≡ ≡ⁿUUTUTTQEAEUUP ⁿUUTUTTDPUEDEUUP ⁿ? ⁿUUTUTTPQEEUUP └? ⁿUUTUPTQEEE@UUP < ⁿUUUUUUUUUUUUUUUUP 3 ⁿUUUUUUUUUUUUUUUUP 3 ⁿUUUUUUUUUUUUUUUUP ⁿUUUUUUUUUUUUUUUUP? ⁿUUUUUUUUUUUUUUUUP? ⁿUUUUUUUUUUUUUUUUP ⁿUUUUUUUUUUUUUUUUP ⁿUUUUUUUUUUUUUUUUS ⁿ ╧ ╧ ╧ ╧ ╧ ╧ ╧ ╧ ≡≡? ≡ ⁿ? ├ ≡ ⁿ └ ≡ ⁿ ≡ ≡ ≡? ≡ ⁿ? ⁿ ⁿ ≡≤≤ ≤ ├ ⁿ ⁿ ? ■ ≤ └≡╧≤≤└ⁿ0 ⁿ ? ² ? ⁿ ≡ ≤ ?33?3≤≤≡ └ ┐ ⁿ ╧ ≤ ≤≤?33?3≤≤≤ ? ⁿ ╧ ≤ ╧ ╦ ≡ ⁿ└≤3ⁿⁿⁿ? ≡ ╧ ╦ ≤ ? ≈ ⁿ┐ ⁿ┐ ≡ ? ≡? ⁿ? ²? ⌠ ? ≡ ⌠ ├ ≡ ≤ ├ ⁿ ⁿ? ? ≡? ≡ â ■ ≡┐ ?? ≤ ≤ ≤≤ ? ├ ■ ≡» └ⁿ ≡ ?3└≡≤ⁿ ≤ └ ??<?ⁿⁿ ╨ⁿC 0 ?3≤≤≡3?ⁿ???╠ ??3≤├ └ⁿO ≡ ?≤ ?3≤≤≤ 3?≤≤???╠ ??3≤? αⁿ ⁿO ≡ ?≤ └≡└ⁿ3?ⁿ└ⁿ≤ⁿ?< ² ± α ? ≡? ≤ └ ? ╧ / ╧ ⁿ?ⁿ ≤ ⁿ? ⁿ ≡? ⁿ? ≤ ± ⁿⁿ ■ └ ⁿⁿ ± ??■ ≤ ⁿⁿ ⁿ ⁿ ⁿⁿ╠?≡≡ ≡? ≤ ??ⁿ ≤ ⁿⁿ ? └ ⁿ├ⁿⁿ╧ⁿ└< ≤ ?? ? ≈ ⁿ ? ⁿ ╧ⁿⁿ╧ⁿ ╧ⁿ ≡ √ ?? ? ≥ ⁿ≤ ²? ≡?ⁿ ╧ ≡└< ≡ ??ⁿ ⁿ?ⁿⁿ ± └ ⁿ ≡ ├ ⁿ? ⁿ K π ⁿÅ └ └ ╦ ⁿ ≡? └ ⁿ ⁿ ±? Ç └ⁿO └ └ └╝ ⁿ? ⁿ ≡? ├ ⁿú ╨? ≥? ⁿ? ≡┐ ±? ╫ ╧ ⁿ? ╙ ╧ ≡ └ ≡? ≡ ■?ⁿⁿ ⁿ ⁿ ⁿ? ??ⁿ? ⁿ ⁿ0 ? ≡≡? ■ ? ? ² ⁿ╠ ┐ ⁿ 3? ┐ ⁿ ⁿⁿ ? ╧ ⁿ ?? ? ⁿ ⁿⁿ ? ╧ ⁿ ?? ? ⁿ┐ⁿⁿ ⁿ ╧ ⁿ ??²? Oⁿⁿ ≡ ╧ ??≡ ≡ ï ╧ ° â ■ ⁿO ╧ ⁿ ⁿ └? ╧ Σ? $ ╧ αⁿ ≡≤ ╧ └? ?╧ ╧ └ⁿ ⁿ ≥ ≤≤ ╧ ╧╧ ⁿ ² ≡ ╚ ? ≤≤├ⁿ└≤└≤≤└? ╧ ╧╧ⁿ └?└? α ╧ ≡≤≤≤?0 ?3≤ ╧ ╧╠≡?╧╧╧╧╧╠ⁿ ╦ ⁿ ╧ ≤ ≤╧≤≤≤?3 ?3≤ ?ⁿ ╧╠ ⁿ ╧╧╧╧╧╠ⁿ ■ ≤ ≤ √ 3 ÷ ≤≤└ⁿ└≤ └ⁿ ╧ └?ⁿ ╧╧╧╧ √ ╠ ⁿ ≤ ⁿⁿ ⁿ ≤ ╧ ⁿ √ ??ⁿ ≤ ⁿ ┐ ╧ ├ ≤ ? ┐ ≤ ⁿⁿ ? ╧ ≤ ?? ? ⌠ ⁿⁿ ⁿ ╧ ⌠ ??ⁿ ⁿ┐ⁿⁿ √ ≤≤ ? ? ├ ╧ ╧╧ ╧ ≡ ╧ ⁿ/ ??≈ ▀ ≡├ ? ? ≤ ╧ ├ ╧ ⁿ ╧ ├ ⁿ? ≤3└ⁿ└≡ⁿ0ⁿ?└<≤ ╧ ╠╧≡ⁿ └? ├ ⁿ┐ ≡ └ ≤≤??└3≤?3≤ ??ⁿ≤ └ ╧╠ⁿ╧╠ⁿ ╧╧╠ⁿ ±? └ ─ⁿ/ ≤≤? ??3≤?3≤? ??≤≤≤ ╧ ╧╠ⁿ╧╠ ⁿ ╧╧╠ⁿ └²O ≤≤└ ╧└0?<?ⁿ└<└ ╧ ╧╧≡≡?╧╧ Ç ─ⁿ ≤ ╧ ⁿ ─ⁿÅ °? ⌠ ≤ ╧ ├ ≥? ⌠ ├ ╧ ╙ ╦ ? ├ ? ├ ╧ ⁿ ╧ⁿ ≡ ╧ ? ╩ ° ²? ⁿ╧ ≤ ≤ ≤ ╧ ≤? ╧ⁿ ⁿ ⁿ ■ ⁿ? ≤ ≤≤ⁿ≤≤≤└ⁿ?└<≤ ╧ ╧╠≡ⁿ ≡<├├<ⁿⁿ ≡?└? ≤ ╧ ╧ ≡?<≤≤≤≤ ??ⁿ≤ └ └ⁿ╧╧ⁿ╧╠?╠╠ⁿⁿ ⁿ ╧╧╠ⁿ ╧ ▀ √ ≤≤?3≤≤≤≤≤ ??≤≤≤ ╧╠ⁿ╧╧ⁿ ╧╠ ╠╠ⁿⁿⁿⁿⁿ ╧╧╠ⁿ ≤ ┐ ≤ ≤≤?<└ⁿⁿⁿ└<└ ╧╠ⁿ≡ⁿ ≡< ╠╧≡? ?╧╧ ? ≤ ? ² ≤ ⁿ ┐ ■ ⁿ ⁿ ├ ⁿ ⁿ @╚ ≤ⁿ? ╠ ?≤ ? ???└ⁿ0≡└ⁿ└ ??≤≡≤≤└??? ???≤≤ ?≤≤???? ?<ⁿⁿ?≤≤└?╧└ └ UU@UUEUUEUUUS ?? ? ⁿUUUEEUTUUUUUUUUT ?<?<└ ±UUUEETU@@U? 3≤???? ±UUUEDTPEEEEEDTU? <≤≤???? ±UUUEDTUEEEEEDTU? ?<└?╧└ ±UUUEDUTUEEEEEDTU? ±UUU@TUEEEEU? └ ±UUUUUUUUUUUUUUTU? └? ? ±UU@AU? └? └? ±UU? ±UU? ⁿ? └? ±UU? ±UU? ├ └ ±UU? ±UU? ? ⁿUT ±UU? ⁿ ⁿ ±UU? ≤ ≡ ⁿ ±UU? ╧ ≤ ±UU? ╧ ≤ ≤ ±UU? ╧ ⁿ? ╧ ±UU? ╧ ╧ ? ±UU? ╧ ≡ ⁿ ±UU? ╧ ≤ ±TU? ╧ ≡ ≤ ±Q? ≤ ╧ ±EE? ≤ ≡? ⁿ? ±@? ≤ └ ≤ ±EE? ≤ ≡ ⁿ ±EE? ⁿ ⁿ ±EE? ⁿ ±UU? ⁿ ±UU? └ ⁿ ⁿ ±UU? ? ≤ ? ±UU? ≡ ⁿ? ╧ ±UU? ╧ ╧ ≤ └ ⁿ ?3 ≡UU? ? ≤ ≤ ??≤≤ ? ?3 ? ┼UUUUUUUUUUU? ? ≤ ⁿ ?≤ 0ⁿ└ⁿ ?0└ⁿ└? UUUUUUUUUUU? ⁿ ⁿ ? ≡?≤≡└?? 33≤└?? ⁿUUUUUUUUUUUU? ≤ ? ╧ ??≤≤?≤ ??? 3≤??? ? ⁿUUUUUUUUUUUU? ≤ ? ≤ └ ⁿ?ⁿ└?╧ ?3≤└?╧ ⁿPUUUUUUUUU? ╧ ╧ ⁿ ⁿUUUUUUUUUT ╧ ╧ ≡? ⁿUUUUUUUUUS ? ≤ └ ⁿU ? ≤ 0? ? ⁿU@S ? ≤ ? └≡ ⁿ ├ ⁿUUS ? ≤ ? ? ≡ ⁿ ⁿ ⁿPS ⁿ ⁿ ⁿ ╧ ⁿ ≤ ⁿUES ⁿ ⁿ ⁿ ╧ ⁿ ⁿUQS ⁿ ⁿ ⁿ? ≤ ╧ ⁿ ⁿUQS ⁿ ⁿ ≤? ≤ ≡ ╧ ≤ ⁿUUS ⁿ ⁿ ≤╠ ≤ ╠ ≤ ≤ ⁿUUS ⁿ ⁿ ⁿ ≤ ╧ ╧3≤ ├ ≤ ⁿTS ⁿ ⁿ ⁿ ╧ ╧ ⁿ 3 ≤ ⁿQQS ⁿ ⁿ ⁿ ╧ ≤ ⁿ <╧≤ ⁿQQS ⁿ ⁿ ⁿ └ ? ⁿ ? ≤ ⁿQQS ? ≤ ? ? ? ╧ ≤ ⁿTS ? ≤ ? ? ╧? ? ≤ ⁿUUS ? ≤ ? ? ≡ ? ╧ ⁿP ? ⁿ ≤ ⁿ ? ? ≤ ╧ ⁿQQS ╧ ≤ⁿ? ╧ ⁿ ╧ ≤ ╧ ⁿQQS ╧ ⁿ ╧ ╧ └ⁿ ╧ ⁿ ╧ ⁿQQS ≤ ╠3 ? ? ⁿ ╧ ≡╧ ⁿTS ≤ ├ ⁿ? ? ⁿ ≤ ╧ ╧ ⁿUUS ⁿ ? ⁿ ⁿ ⁿ ╠ ╧ ⁿ ╧ ⁿUUS <ⁿ≡3 ≤ⁿ ⁿ≤ ≤ ≡╧╧ ⁿQU ├ ⁿ ⁿ ≤ ≡╧╧ ⁿP ╧ ? ≤ ≡╧╧ ⁿQUS ? ≤ ⁿ?? ⁿUUS ? ≤ ? ⁿUUS ? ≤ ⁿ? ⁿTS ├ ╧ ≤ ≤ ? ⁿQS ╧ ≤ ≤ ? ⁿQS └ ╧ ⁿ≤ ≤ ≤ ? ⁿQS ? ≤ ≡ ≤ ≡? ⁿUS └ ≤ ⁿ ╧ ? ⁿUUS ? ≤ ╧ ⁿ? ⁿPS ≤ ╧ ≤ ? ⁿUQS ⁿ ╧ ≤ ? ⁿPS ⁿ ⁿ3 ? ≤ ╧ ⁿUQS ⁿ ⁿ3 ? ≡╧ ⁿPS ? ⁿ3 ? ╧ ⁿUUS ? ╧ ? ╧ ⁿUUS ╧ ⁿ ╧╧ ⁿUUS ⁿ ╧ ⁿ 0≤ ⁿUUS ⁿ ╧ ⁿ ⁿ ≤╧≤ UO ⁿ ╧ ⁿ ≤ ≤ ┼U? ╧ ⁿ ≤ ⁿ ≡ ╧ └≤ ⁿ ├ ╧ ╧ ≤╧ⁿ < ╧ └╧ ≤╧ⁿ < ╧ ╧╧ ≤╧ ? < ? ?? ⁿ? ? ├ ? ╧? ╧ ? └? ≤ ⁿ ? ? ? ≤ ┴U ⁿ╧ⁿ ? ⁿ US ⁿ╧ⁿ ⁿ ? US ⁿ ⁿ ⁿ ╧ ⁿUUT ≡? ≡ ⁿ ⁿ ≤ ╧ ⁿUUT ╧╧ ╧ⁿ ≤ ≤ ≤ ≤ ⁿUUT ╧ ≡ⁿⁿⁿ ≤ ≤ ⁿ ≤ US ╧ⁿⁿ└?╧ⁿⁿⁿ ≤ ≡ ⁿ US ╧╠ⁿ ╧╧ⁿⁿⁿ ╧ ⁿ ┴U ≡?└?≤≡? ╧ ⁿ? ⁿ ⁿ ⁿ ├ ╧ ≤╧ ⁿ ? └? ⁿ ├ < ╧ ≤╧ ? ? ╧╧ ⁿ < ? ≤╧ ? ? ╧╧≡? └ < ? ⁿ? ? ? └ⁿ≡ⁿ ≡? ├ ? ? ? ╧<ⁿ╧╠ⁿ ? ? ? ╧╧≡ ⁿ ≡ ? < ? ? ├ < ? └ ? ╧ ? <ⁿ ⁿ ? ╧ ╧╧ ⁿ <ⁿ ⁿ ╧ ├ ╧ ≤ ├ⁿ ⁿ ╧ ╠╧≡ ╧ ⁿ ⁿ ╧ ╧╠ⁿ└?╧ ? ⁿ ⁿ ≤ ╧╠ⁿ ╧╧ ⁿ ⁿ ≤ ≤ ╧╧└?≤ ≤ ⁿ ≤ ≤ ╧ ⁿ ≤? ≤ ≤ ╧ ⁿ ≡╧ ≤ ⁿ └ ≡ ╧ ╧ <ⁿ ≡╧ ≤ ⁿ ⁿ ╧ⁿ ╧ ╧ ⁿⁿ ≡╧ ≤ ?ⁿⁿ├≡<ⁿ≡?╧ⁿ ≡ ╧ ?ⁿ ⁿ╧ ╧ ╧ⁿⁿ?≡3└╧ⁿⁿ╧╧ ? ⁿ ╧ ╧ⁿⁿ ╧╧3╧ ╧ⁿⁿ ╧╧ ? ⁿ ? ≤ⁿⁿ ≡╧≡?≡?≡ ? └ⁿ ⁿ ? ⁿ ? ⁿ ≤ ? ⁿ ? ⁿ ⁿ ⁿ ? ⁿ ≡ ⁿ ≤ ? ⁿ ⁿ ? ≤ ? ≤ └ ╧ ≤╧ ≤ └ ≤ ? ╧ └? ≤ ⁿ ╧ ? ╧ ≤ ≤ ≡ ? ? ╧ ╧ ⁿ ≡ ╧ ╧ ≤ ├ ╧ ⁿ ╧ ⁿ ⁿ? ≡ ≤ ≡╧ ? ? ≤ ≤ ≡╧ ? ? ⁿ ╧ ≤ ≡╧ ? ? └ ≤ ⁿ ? ? ╧ └? ≡ ? ?? ≡ ╧≤ ≤ ≤ └? ⁿⁿ ? ≤ ≤≤ ? ? ╧ ≤ ⁿ ?ⁿ?0ⁿ└ ≤≤└ ?├≡├ⁿ├ⁿ ╧ ≤ ⁿ ?≡≤ ≤≤<≤≤≤≤ ?≤≤≤?? ╧ ≤ ⁿ ? ?? ≤≤ ≤≤? ?≤≤≤≤ ?≤≤≤?? ╧ ⁿ ?ⁿ?≡ⁿ ≡└ ?└≤≤└ ╧└ⁿ?? ≤ ⁿ ≤ ⁿ ≤ ? ? └ ╧ ⁿ ? ? ? ╧ ? ? ⁿ └ ? ? ├ ≡ ⁿ ╧ ? ? ├ ? └? ≡? ? └? ? └? ⁿ ? └└ ? ≡? ╧ ╧ ≤ ≤ ≤ @╚ ≡ ⁿ? ⁿ ╧ ≤ ≤ ╧ⁿ╧ⁿ ?ⁿ3 ? 0╧ ?ⁿ3 ? 3 ⁿ╧ ⁿ ⁿ3 ╧ 0╧ ⁿ 3 ╧ 0UUUUUUP╧ ≤ ≤ 0UUUUUUP╧ ≤ ? ≤ 0UUUUUUP╧ ≤ ⁿ3 ≤ 0UUUUUUP╧ ╧ ⁿ3 ⁿ 0UUUUUUP╧ ╧ ⁿ3 ⁿ 0UUUUUUP╧ ╧ ⁿ 0UUUUUUP╧ ?? ≤ ? ? 0UUUUUUP╧ ?? ≤ ? ? 0UUUUUUP╧ ?<0ⁿ?<0ⁿ ? ≤ ? 0UUUUUUP╧ <≤≤?<≡ ? └ ? 0UUUUUUP╧ ?3≤?≤≤33≤?≤ ? ╧≤ ? 0UUUUUUP╧ ?<?ⁿ╠ⁿ?ⁿ ⁿ ╧ 0UUUUUUP╧ ⁿ ╧ 0╧ └ ⁿ≤ ╧ 0╧ ⁿ ⁿ≤ ╧ ? ╧ ⁿ ⁿ≤ ╧ ⁿ ⁿ≤ ╧ ? ╧ ⁿ ╧ ? ╧ └ ⁿ ⁿ ╧ ?? ≤ ? ⁿ ╧ ⁿ0 ?ⁿ≤ⁿ?<0ⁿ ⁿ ≤ ╧ ≡<╧ 3╠ └3≤└ ??<≡ ⁿ ╠ ╧ └≤ ├≤? ?3≤≤ ?33≤?≤ ⁿ ⁿ≤ ╧ ├? ╠ └ⁿ≤ ╧╠ⁿ?ⁿ ⁿ ╧ ⁿ ├ ⁿ ╧ ? ⁿ ≡ └ ╧ ⁿ └ ⁿ ? ⁿ ? ≡? ⁿ ? ⁿ ? ?└ └ ? ⁿ ? ? ? └ ? ≡ ? ? ? ╧ ? ⁿ ├ ╧ ⁿ3 ⁿ ⁿ ╧ ⁿ3 ⁿ ≤ ⁿ3 ≤ ≤ └ ⁿ ≤ ≤ ⁿ ⁿⁿ ≤ ≤ ? ⁿⁿ≡ⁿ≡ ⁿ └? ╧ ╧ ⁿⁿⁿⁿⁿⁿ╧╠ ⁿ ╧ ╧ ≤ ⁿⁿⁿⁿⁿⁿ╧╧ⁿ ? ≤ ? ⁿ ⁿⁿⁿ≡<ⁿ≡ ? ╧ ? ? ╧ ╧└?ⁿ ? ⁿ? ≤ ≤ ? ╧ ⁿ ╧ ?? ? ? ≤ ⁿ ⁿ? ?<└<0ⁿ?└< ≤ ╧ ≡ 0 ? ?? ? ⁿ ╧ <≤ ??? ?? ? ? ╧ ? ?< ╧?ⁿ└?╧ ? ╧ ? ? ╧ ? ╧ ╧ ? ╧ ╧ ? ≤ ╧ ? ≤ ⁿ ╧ ╧ ? ≤ ≤? ⁿ ╧ ? ⁿ ╧╧≡?≡<≡ ╧ ? ⁿ └ ⁿ ╧╧╠ⁿ└? ╧ ? ⁿ ╧╠ ⁿ ╧╧╠ⁿ ╧ ╧ ? ⁿ ╧╧ ?≡<ⁿ└? ╧ ? ? ╧ ? ? ╧ ⁿO ? ⁿ ±S ? ╧ T? ? ╧ ⁿUUO ≡ ╧ ±UUS ⁿ ╧ ┼UUT ? ╧ UUU? ╧ ⁿUUUUC ╧ ┴UUUUT ╧ UUUUU? ╧ ⁿUUUUUUO ╧ ±UUUUUUS ╧ ┼UUUUUUT? ╧ UUUUUUUO ╧ ≡UUUUUUUUS ╧ ┼UUUUUUUUT ╧ UUUUUUUUU? └ ⁿUUUUUUUUUUC ⁿ ⁿ? ≡ ±UUUUUUUUUUT └ └ ┼UUUUUUUUUUU? ⁿ? ≡ ? ≡ ⁿUUUUUUUUUUUO ≡ ? └ ⁿ ±UUUUUUUUUUUUS ⁿ └ ≡? ≡? ┼UUUUUUUUUUUUT? ⁿ └ UUUUUUUUUUUUUO └ ⁿ ├ ⁿUUUUUUUUUUUUUUS ⁿ? ≡ ? ≤ ±UUUUUUUUUUUUUUT ≤ ? ⁿ ╧ ⁿ ╧ ⁿ UQQ@PU@QQ@UU? ╧ ╧ ≤ⁿⁿ╧ ╧ ⁿ ? ⁿUUPAQQUQPQUC ? ⁿ ? ├ ≤ ╧ⁿ └?╠?≡≡<├≡ ≡?≡ ╧ ±UUQQQUQQUUT ⁿ ≤≤ ? ≤ ⁿ ╧ⁿ ╧╧├ ╧ ╧└?ⁿⁿⁿ ╧╧ⁿ ╧└UUQQQQUQQUUⁿ ≤ ?0╧ⁿ≤ⁿ ⁿ ╧ⁿⁿ╧╠ⁿ╧ⁿⁿ╧ ╧╧ⁿ ⁿ ⁿⁿ ╧╧ ⁿ ╧ ±UUQQQQUQQAUU? ⁿ ⁿ?33?3≤≤≡ ⁿ ≤ ╧╧╧ ≡≤≡< ≡< ?≡ ? ⁿUUQQ@P@QQ@UUT ? ≤≤?33?3≤≤ ≤ ≤ ⁿ ⁿ UUUUUUUUUUUUUUUC ╧ ⁿ└33ⁿ└≡ ╧ ? ≤ ±UUUUUUUUUUUUUUT? ≤ ? ? ├ ⁿUUUUUUUUUUUUUUP ⁿ? ≡ ≡ ⁿ └ UUUUUUUUUUUUUC └ ⁿ ≡? ≡? ┼UUUUUUUUUUUUU? └ ⁿ ±UUUUUUUUUUUUT ⁿ └ ? ≡ ⁿUUUUUUUUUUUC ≡ ? └ ┼UUUUUUUUUUU? ⁿ? ≡ ⁿ? ≡ ±UUUUUUUUUUT └ └ ⁿUUUUUUUUUUC ⁿ UUUUUUUUU? ⁿ ┼UUUUUUUUT ⁿ ≡UUUUUUUUC ⁿ UUUUUUU? ⁿ ≡? ╧ ┼UUUUUUT ⁿ ╧╧ ╧ ±UUUUUUC ⁿ ╧ ╧╠≡ ⁿUUUUUU? ⁿ ≡ⁿ╧╠ⁿ╧╠ UUUUT ⁿ ╧╠ⁿ╧╠ⁿ╧╧ⁿ ±UUUUC ⁿ ≡?≡ⁿ≡ ⁿUUUU? ⁿ UUT ⁿ ┼UUC ⁿ ±UU? ⁿ ⁿT ⁿ ≡? ≡ ┼S ⁿ ╧╧ ╧ⁿ ±O ⁿ ╧ⁿ3≡?╧ⁿ ⁿ? ⁿ ≡╠└╧ⁿⁿ ? ⁿ ╧╠╠╧ ╧ⁿ ⁿ ? ⁿ ≡<╠≡?≡< ? ⁿ ? ⁿ ? ⁿ ? ⁿ └ ? ⁿ ⁿ ╧ └ ⁿ ? ⁿ ╧ ⁿ ⁿ ≡≡? ⁿⁿ ? ≤? ⁿ ⁿ ⁿ └?╧└ ⁿⁿ≡ⁿ≡ ? ╧╧≡?≡<≡ ⁿ ⁿⁿⁿ ╧╧╧ ⁿ ⁿⁿⁿⁿⁿⁿ╧╠ ? └ ⁿ ╧╧╠ⁿ└? ⁿ ⁿ └?≤≡< ⁿⁿⁿⁿⁿⁿ╧╧ⁿ ? ╧╠ ⁿ ╧╧╠ⁿ ╧ ⁿ ⁿⁿⁿ≡<ⁿ≡ ? ╧╧ ?≡<ⁿ└? ⁿ ╧ ? ⁿ ⁿ? ? ⁿ └ ? ⁿ ⁿ ╧ ≡ ⁿ ⁿ ≤╧╧╠├≡? ≤ ≤ ⁿ ⁿⁿⁿ?╧╧╠?└ ≤ ≤ ⁿ ⁿⁿ ⁿ?╧╧╠ ╧ ⁿ ≤ ≤ ⁿ ⁿ ≤╧≤≡ ≡< ≤ ≤ ⁿ ≤ ≤ ⁿ ≤ ≤ ⁿ ≤ ≤ ⁿ ≤≤ ? ≤ ≤ ⁿ ≤≤ ? ≤ ≤ ⁿ ≤≤└≤└< ≤ ≤ ⁿ ≤3?0 ?0 ≤ ≤ ⁿ ≡├?3 ??≤ ≤ ≤ ⁿ ≤≤└≤ └0 ≤ ≤ ⁿ ≤ ≤ ⁿ ≤ ≤ ⁿ ≤ ≤ ⁿ ≤ ≤ ⁿ ≡? ≤ ≤ ⁿ ⁿ ≤ ≤ ⁿ ⁿⁿ3≡?≡? ≤ ≤ ⁿ ⁿⁿ╠≡ⁿ└ ≤ ≤ ⁿ ⁿⁿ╠╧╠ⁿ╧ ⁿ ≤ ≤ ⁿ ≡<╠≡≡< ≤ ≤ ⁿ ⁿ ≤ ≤ ⁿ ├ ? ? ⁿ └ └ ⁿ ≤ ≤ ⁿ ╧╧ ⁿ ⁿ ├╧ ⁿ ⁿ ? ├ ⁿ ╠╠ⁿ├<≡<├≡ ≤≤ ? ≤ ⁿ ╠╠ⁿ╠╠ⁿ└?└? ≤ ?0╧ⁿ≤ⁿ ⁿ ╧ⁿ╠╠ⁿ╧ⁿ ╧ ⁿ?33?3≤≤≡ ⁿ ╧╧╠╠≡< └? ≤≤?33?3≤≤ ≤ ⁿ ⁿ└33ⁿ└≡ ⁿ ? ≡ @╚ ≤≤ └ⁿⁿ3≤?< ╠≤ ?3≤???≤≤≤3≤ ?3 ?≤≤???≤≤≤33 3 03≤??≤≡?< ?3 ?3≤< ?≤≤≤?3≤ ?0└ⁿ?<≤≤≤?< ? ╧ ⁿ ≤ ⁿⁿⁿⁿ ╧ ⁿⁿⁿ ⁿⁿ ╧ ╧ ⁿ ≤ⁿ ≡?└? └<ⁿ ⁿ ≡?└?ⁿ ≡?╧╧╧≡ └? ? ≤ ⁿⁿ╧╠╧╠ⁿ└ⁿⁿ╧╧ ╧╧╧╧╧╧ⁿⁿⁿ╧╠ ? ⁿⁿⁿⁿⁿ ╧╧ ╧╠ⁿ ⁿⁿⁿⁿ ╧╧ⁿⁿ╧╧╧╧╧╧ⁿⁿⁿ╧╧ⁿⁿ ? ?└? └? ?└? ≡?≡≤≡?╧╠≤ ╧ ⁿ ╧ ╧ ├ ╧ ⁿ ⁿ ≡ ⁿ? └ └? ≡? └? ≡ └? ⁿ └? └ └ ≡? ⁿ ⁿ ≡? └ └ ≡? ⁿ ⁿ ≡? ├ └ ≡? ≡? └ ├ ⁿ? ⁿ ≡? ≡ ├ ⁿ ⁿ ├ ≡? ≡? └ └ ≡ ≡ ⁿ < ≡US ≡≤ ⁿUUT ├ UUUU └UUUUUC └UUUUUT? ≡UUUUUUUO ⁿUUUUUUUUP UUUUUUUUUU? ╧ ╧ ⁿ └UUUUUUUUUUUO ╧ ⁿⁿ ╧ⁿ └UUUUUUUUUUUP ⁿ ⁿ ╧ ≡≡ⁿⁿ≡?≡?╠<≡ ≡UUUUUUUUUUUUU? ⁿⁿ ╧ ⁿⁿ ╧ⁿ ╧ⁿⁿ╧╧╧╧ ⁿ≡╧ⁿⁿ├ⁿⁿ└? ⁿUUUUUUUUUUUUUUC ⁿⁿ≡?≡?ⁿⁿ≡?≡?╠<≡ ╧ⁿⁿ╧╧╧╧ ⁿ ╧╧╧ⁿⁿ ╧ⁿⁿ ╧ UUUUUUUUUUUUUUUT ⁿⁿ≡╧≡ⁿ≡╧ⁿⁿ├ⁿⁿ└? └≡≡ⁿ ≡≤ ?╧ⁿⁿ└? └UUUUUUUUUUUUUUUUU ⁿⁿ╧╧╧╧╧ⁿ ╧╧╧ⁿⁿ ╧ⁿⁿ ╧ ╧ ≡P@PQUS ⁿ≡≤≡ⁿ ≡≤ ?╧ⁿⁿ└? ⁿ? UQUQQTEQUQT ≡UUQUQQQQQUUU? ╧ UPQPQUU@ ╧ ≡UQUEQQQQUQU? ╧ ? ╧ ≤ ? ╧ ≤ ╧ QU@QQQQTP ╧ ? ╧ ≤ ? ╧ ≤ ╧ ┴UUUUUUUUUUUUUUUUU ╧ ? ╧ ≤ ? ╧ ≤ ╧ ⁿUUUUUUUUUUUUUUUUP ╧ ? ╧ ≤ ? ╧ ≤ ╧ UUUUUUUUUUUUUUU ╧ ╧ ┼UUUUUUUUUUUUUUP ╧ ╧ ≡UUUUUUUUUUUUUUO ╧ ⁿ 0 ╧ UUUUUUUUUUUUT? ╧ ≡ ⁿ? ≤ⁿ ⁿ╧? ≤? ╧ ┼UUUUUUUUUUUUC ╧ ≤< ⁿ╧? ? ≤ⁿ ⁿ╧? ≤╧ ╧ ≡UUUUUUUUUUUT? ╧ ≤< ⁿ╧? ≡ ≤ⁿ ⁿ╧? ≤? ╧ UUUUUUUUUUC ╧ ≤< ⁿ╧? ╧ ⁿ≤ ╧ ┴UUUUUUUUUT? ╧ ⁿ ╧ ≡UUUUUUUUUC ╧ ≡ ╧ UUUUUUUU? ╧ └ ╧ ≤ ≤ ╧ ┼UUUUUUUP ╧ ≤╧ ⁿ ? ╧ ⁿ ╧ ≡UUUUUUU ╧ ≡ ╠ ? ╧ ⁿ≤ ⁿ ╧ UUUUUP ╧ ≤ ╠ ? ≡? ╧ ⁿUUUU ╧ ≡ ╧ ≡UUP ╧ ⁿ ⁿ ╧ ≡U ╧ ≤ ╧ ≤ ╧ └ ╧ ╧ ≤ ⁿ ≤ ≤ ⁿ ⁿ ╧ ⁿ ≤ ≤ ⁿ ⁿ ╧ ⁿ ? ╧ ≤╧ ⁿ≤ ⁿ ≡? ⁿ ╧ ⁿ ? ╧ ⁿ ╧ └ⁿ ? ╧ ≡ ╧ ⁿ ╧ ?ⁿ ? ╧ ≤? ? ⁿ≤ 0 ⁿ ╧ ?ⁿ ? ╧ ≤ ⁿ├ < ╧ ⁿ? 0 ⁿ ╧ ?ⁿ ? ╧ ≤ ⁿ├ < ╧ ⁿ 0 ⁿ ╧ ⁿ ?└ ╧ ≤ ⁿ├ < ⁿ ╧ ⁿ ?╠≤ ╧ ⁿ╧ ╧ ├ ╧ⁿ ⁿ╧ ├ⁿ ?╠≤ ╧ ⁿ ⁿ └ ⁿ ≤ ╧ <ⁿ ?╧≤ ╧ ⁿ╧ ├ ≤ ≤ ? ⁿ ≤ ╧ <ⁿ ?╧≤ ╧ ⁿ├ 0 ≤ ≤ ≤? ⁿ ≤ ╧ <ⁿ ? ╧ ⁿ├ 0 ≤ ≤ ≤? ├ⁿ ≡╧ ├ⁿ ? ╧ ⁿ├ 0 ≡? ⁿ ⁿ ⁿ ╧ ⁿ ?╧≤ ╧ 3 ≤ <ⁿ ⁿ?╧ ⁿ ?└ ╧ ⁿ? 3 <ⁿ ≤╧╧ ⁿⁿ ?╧ ╧ ≤╧ ⁿ≤ 0 <ⁿ ≤╧╧ ≤ⁿ ? ≤ ≤╧ ╠≤ 0 <ⁿ ≤╧╧ <ⁿ ? ╧╧ ⁿ ⁿ ≤╧ ╠≤ 0 ├ⁿ ⁿ?╧ ⁿ ?≡ ├╧ ⁿ ⁿ ≤╧ ≡ ╠ ⁿ ╧ ⁿ ?╠? ╠╠ⁿ├<≡<├ └ⁿ ╧ ⁿ ?╠? ╠╠ⁿ╠╠ⁿ└? ⁿ╧ ?ⁿ ╧╧ <ⁿ ?╠? ╧ⁿ╠╠ⁿ╧ⁿ 3 ╧ ⁿ├ ?ⁿ 0╧ ⁿⁿ ?ⁿ ╧╧╠╠≡< 0 ⁿ ⁿ├ ?ⁿ ≤╧╧ ?ⁿ ? 0 ≤╧ ⁿ├ ⁿ ╧ ⁿ ?≡ 0 3 ⁿ ╧ ⁿ ?╧? └ ╠ ╧ⁿ ≤?╧ ⁿ ?╧? ?? ? ⁿ? ⁿ ≡╧╧ ⁿⁿ ?╧? ?≤≤└<└≡╧└? ≤ ⁿ ≡╧╧ ≤ⁿ ?╧? └3≤ ?33 ≤ ⁿ ≡╧╧ <ⁿ ? ?3≤ ???≤3 ? ≤ ├ⁿ ⁿ╧╧ ⁿ ? └ⁿ ╧└≤3 ? ⁿ ╧ ⁿ ? ? ≤ ⁿ ╧ ⁿ ?≡ ≡ ⁿⁿ ╧╧ <ⁿ ?╧? ? ⁿⁿ 0╧ ⁿⁿ ? ╧ ⁿⁿ ≤╧╧ ?ⁿ ? ╧ ⁿ ╧ ⁿ ?└? ⁿ ╧ ⁿ ?ⁿ ≤╧╧ ╧ⁿ ? ? ≤? <ⁿ ≤╧╧ ⁿ ? ? ≤ <ⁿ ≤╧╧ ⁿ ? ≤ <ⁿ ≤╧╧ ⁿ ? ≤ ├ⁿ ⁿ?╧ ├ⁿ ? ⁿ╧ ⁿ ╧ ⁿ ?╧? ╧ⁿ ⁿ ╧ ├ⁿ ?└3 ⁿ ≡╧╧ <ⁿ ?╧ ⁿ ≡╧╧ <ⁿ ? ⁿ ≡╧╧ <ⁿ ? ├ⁿ ⁿ?╧ ?≡ ⁿ ╧ ⁿ ?╧? ⁿ├ⁿ └?╧ ╧ⁿ ?╧? ≤╠ⁿ ?╧╧ ⁿ ?╧? ≤╠ⁿ ?╧╧ ⁿ ?╧? ≤╠ⁿ ?╧╧ ⁿ ? ⁿ3ⁿ ╧ ├ⁿ ? ⁿ ╧ ⁿ ?╧? ⁿ ╧ ⁿⁿ ?└3 ⁿ ╧ ≤├ⁿ ?╧ ⁿ ╧ ≤╧ⁿ ? ⁿ ╧ ≤╧ⁿ ? ⁿ ╧ ≡ⁿ ? ⁿ ╧ ⁿ ? ? ≤ ?≡ └ ≤ ?╧? ?? ≤ ? ?0 ≡ ⁿ └? ≡ ? ⁿ ?3≤ ≤ ⁿ ≤ ╧ ? ≤ ⁿ ?≡? ⁿ ?3≤ ≤ ⁿ ╧ ? ≤ ⁿ ?╧ ⁿ └≤≤ ≤ ╠ ╧ ? ≤ ⁿ <╧ ⁿ ╠ └? ?≡ <╧ ⁿ ╠ ⁿ╧ 3 ?? ⁿ ≤ └? ≤? ? ⁿ ╧? ╠ ≤? ? ⁿ └ ╧ⁿ ? ╧ ╧? 3 ⁿ╧ ? ⁿ ???≤ ╧? 3 ⁿ╧ ? ⁿ ???≤ ╠ ╧? 3 3 ? ⁿ ?<└ ≡ ╠ 3 3 ? ? ⁿ ???≤ ╠ ≡≡≡ 3 3 ? ?? ⁿ └ ?≤ ≤ ⁿ 3 3 ? ?<?ⁿ0≤≤ ⁿ └? ⁿ≡ ≡≤ ╠ 3 ? ???<≤≤ ⁿ ╧ ? ⁿ ╠ 3 ? ????3≤?≤≤ ⁿ └? ≤? ⁿ╧ ? ⁿ?<?ⁿ ⁿ ╠ ≡ ⁿ├ ≤? ? ≤ ⁿ ╠ ≤ ╧ ? ⁿ 3 ╠ ? ⁿ ╠ ≤ ╧ ? ⁿ ≡ ≤ ? ⁿ ≤ ≤ ╧ ? ⁿ ≤ ⁿ ≡ ≤ ╧ ? ⁿ ≤ ⁿ ≤ ⁿ ≡ ≤ ⁿ ≡ ≡ @╚ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUS¼ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UPEDEDPTPUSⁿ ⁿ UEDTATEEETTEEUSⁿ ⁿ UETTDDTEEETTDEUUSⁿ ⁿ UETTEDEEETTDDUSⁿ ⁿ UEDTEDUEEETTPEEUSⁿ ⁿ UPEDUPEPTPUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ UUUUUUUUUUUUUUUUSⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ⁿ ≡ ⁿ ≤ ╠ ⁿ ≤╠ ⁿ≤≤≤≤≤≤≤≤? ╠ ⁿ╠ ⁿ╠╠╠╠╠╠╠≤? »╠ ⁿ╠ ⁿ╠╠╠╠╠╠╠≤? ╠ ⁿ╠ ⁿ╠╠╠╠╠╠╠≤? ╧ ╠ ⁿ╠ ⁿ╠╠╠╠╠╠╠≤0╠ ⁿ╠ ⁿ╠╠╠╠╠╠╠≤? ╧ ╠δ ⁿ╠ ⁿ╠╠╠╠╠╠╠≤? ╠ ⁿ╠ ⁿ╠╠╠╠╠╠╠≤╠ ⁿ≤≤≤≤≤≤≤≤ ╠ ⁿ ≡ ⁿ ⁿ ⁿ ≡ ⁿ ⁿ ├ ├ ⁿ ⁿ└≡ ⁿ0╠├╠╠╠╠╠╠╠╠╠╠├╠<? ≡├3333333333330├3 ├╠0╠╠╠╠╠╠╠╠╠╠╠╠0╠├├ 30├33333333333330≡ ⁿ0╠├╠╠╠╠╠╠╠╠╠╠╠╠├╠<? ≡├333333333333330├3 ├<≡├ ╧ ≡ └? ╧ ? └? ⁿ ⁿ ⁿ ⁿ ⁿ ? ? ? ? ? ? ≡ ╧ ╧ ? ? ⁿ ╧ ⁿ ? ? ⁿ ≡╠?≡≡<ⁿ ? ?ⁿⁿⁿ╧ ╧├ ╧╧ ╧ⁿⁿⁿ ? ?ⁿ ⁿⁿ ╧ ╧╧ ╧╧ ╧ⁿⁿⁿ ? ? ≡?≡≤╧ ≡ ? ? ? ⁿ ? ? ├ ? ? ? ? ? ? ⁿ ⁿ ⁿ ⁿ ⁿ ? ? ? ? ? ? ? ? ? ? ≤ ? ? └<?0ⁿ?<?└ⁿ ? ? ? ?≤ ???≤≡ ? ? ? ??≤ ???≤ ≤ ? ? └<?ⁿ└<ⁿ≡ ? ? ? ? ? ? ? ? ? ? ⁿ ⁿ ⁿ ⁿ ⁿ ? ? ? ? ? ? ╧ ? ? ╧ ╧ ? ? ≡≡<3└?╧≡<├≡ ? ? └<└╠╧╧╧└?└? ? ? ⁿⁿ ╧ⁿ╧ⁿ╠╧╧╧╧ⁿ ╧ ? ? └<≡<╠└?≡< └? ? ? ? ? ? ? ? ? ? ? ⁿ ⁿ ⁿ ⁿ ⁿ ? ? ? ? ? ? ?├ ? ? ≤ ? ? ⁿ└≡╧ⁿ?≤ⁿ0ⁿ ? ? ≤ ?33???≤≡≡ ? ? ≤ ?33???≤≤ ? ≤ ? ? ⁿ└≤3ⁿ└ⁿ?≡ ? ⁿ ? ? ? ≡ ⁿ ≤ ? ? ? ≤ ╧ ⁿ ≤ ? ? ≤ ╧ ⁿ ⁿ ⁿ ≤ ? ? ≤ ≡ ╧ ╧ ⁿ ⁿ ⁿ ≤ ? ≤ ⁿ ⁿ ╧ ⁿⁿ≡╧╧≡?≡?≡?≤ ⁿ ≤ ≡ⁿⁿⁿ≡?≡<≡ ╧ ⁿⁿⁿ└<╧╠ⁿ╧╠ ╧╠ⁿ└≥» ⁿ ·ú └<ⁿⁿⁿⁿⁿ ╧╧╠ⁿ└? ╧ ⁿⁿⁿ ╠ ╧╠ⁿ╧╠ ╧╠ⁿ╧ ≤·» ⁿ ■¬│ ╠ⁿⁿⁿⁿⁿ ╧╧╠ⁿ ╧ ╧ ⁿⁿ└?≡≡?≡?≡?≤ ·» ⁿ ·½■≤ └?≡? ?≡<ⁿ└? ╧ ⁿⁿ ≤ ·½ ⁿ ·» ≤ ╧ ⁿⁿ ≤ ■½ ? ·» ≤ ╧ ⁿ ≤ ■¬ ? ? Ω» ≤ ╧ ⁿ ≤ ¬ ? ? Ω┐ ≤ ╧ ⁿ ¬ ? ? ¬┐ ≡ ⁿ ¬┐ ? ? ¬ ⁿ Ω╗? ≤└ⁿ0ⁿⁿ ?¬ ╧ ⁿ Ω? ?0 ?3≤ⁿ30 * ╧ ╧ ⁿ ¬? ?3 ?3≤?≤≤3?≤ ? ≡?╠? ⁿ ? ≤ └ⁿ?ⁿ30 ? ╧≡├ⁿ ⁿ ? ? ≤ ? ╧╧╧ⁿ└ ⁿ ⁿ ? ? ? ≤≡╧< ⁿ ? ? ⁿ ? ? └ ? ≤ ╧ ≤ ╧ ╧ ╧ ≤ ╧ ⁿ ⁿ ╧ ╧ ╧ ≤ ╧ ⁿ ⁿ ≡ⁿ└?≡?╠? ≤ ╧ⁿ≡╧╧≡?≡?≡? └<ⁿ╧╧╧≡├ⁿ ≤ ╧ⁿⁿ└<╧╠ⁿ╧╠ ╧╠ⁿ└ ╠ⁿ╧╧╧╧╧ⁿ└ ⁿ ≤ ╧ⁿⁿ ╠ ╧╠ⁿ╧╠ ╧╠ⁿ╧ └?└?≤≡╧< ≤ ╧ⁿ└?≡≡?≡?≡? ≤ ╧ⁿ ⁿ ╧ⁿ ╧ └ ≤ ≤ ≤ ⁿ ?╧ ╧ ≤ ╧ ⁿ ≤ ≡└?≡ⁿ╧╧ ╠?ⁿ └?└? ≤ ╧ⁿⁿ╧╧╧ⁿⁿⁿ╧╠ ├ⁿ≡?╧╧╧╧╧╠ⁿ ≤ ╧ⁿⁿ╧╧╧ⁿⁿⁿ╧╠ ╧ⁿ ⁿ ╧╧╧╧╧╠ⁿ ≤ ≡╧╧≤≡<ⁿ≡ ╧ ⁿ ╧╧╧╧ ≤ ⁿ ≤ ├ ≤ ≡ ⁿ?? < ⁿ???3≡ⁿ ?0≡?ⁿ├?30?ⁿ≤<≤└? ≤≡)Q╔Aæ╣1⌐!qÖ9ëQí±i╣⌐∙q┴9 ▒ ) í æ Y⌐∙Ö ╡¥ uy¥Qm¡9╣íσíë=ü=ì ┘Q ) ▌∙ EòßÖ▒ 1AT EASE begins with a discussion of the kinds of 2thinking built into computers and the modes of 3thinking required to use one. 1The fundamental problem in working with computers 2is that they require us to translate our three 3dimensional world into two dimensional symbols. 1This requires the use of a number of different 2modes of thinking. 1This requires the use of a number of different 2modes of thinking. 4 Rigorous: precise and accurate 1This requires the use of a number of different 2modes of thinking. 4 Metaphorical: connecting unrelated ideas 5 to produce new insights 1This requires the use of a number of different 2modes of thinking. 4 Analytical: breaking down a problem in a 5 methodical manner 1In addition, the "Thinking" lesson also introduces 2a problem-solving method: 1In addition, the "Thinking" lesson also introduces 2a problem-solving method: 4 Defining: clearly stating your problem 1In addition, the "Thinking" lesson also introduces 2a problem-solving method: 4 Modeling: representing your problem with 5 symbols 1In addition, the "Thinking" lesson also introduces 2a problem-solving method: 4 Formulating: Generating step-by-step 5 instructions (algorithm 6 development) 1Defining is stating your problem as clearly as 2possible. This is the key to success in problem 3solving. 1When defining, you will work with three general 2types of problems. 1When defining, you will work with three general 2types of problems. 4 Conceptual: problems of ideas (e.g., what 5 is a better mousetrap?) 1When defining, you will work with three general 2types of problems. 4 Technical: problems of the working world 5 (e.g., how do we build the 6 better mousetrap?) 1When defining, you will work with three general 2types of problems. 4 Apparently unsolvable problems 1In dealing with the conceptual problem, we ask 2"What do we mean?" It's crucial we make sure each 3idea expressed──each word used──means the same 4thing to everyone involved. 1Even when working alone, it is important to 2make sure we have not masked ambiguity with 3a lazy problem definition. 1When dealing with technical problems, the question 2to ask is "What if?" What if someone types in the 3wrong information? What if people can't 4understand the instructions? What if our assets 5reach a billion dollars? What if....? 1And finally, when dealing with the apparently 2unsolvable problem, we ask "What's for dinner?" 3This is a tongue-in-cheek way of saying, "Leave 4the problem, step back, and then redefine it from 5a different reference point." 1Modeling is the representation of things and 2actions using symbols. 4 (e.g., An entire baseball game can be 5 modeled by: Tigers 7, Twins 5.) 1In this lesson, we learned how to select: 1In this lesson, we learned how to select: 3 ∙ The characteristics of things and 4 actions we want to model 1In this lesson, we learned how to select: 3 ∙ The vehicles with which we will create 4 our models 1In this lesson, we learned how to select: 3 ∙ And the symbols we will use to represent 4 our selected characteristics 1In this lesson, we learned how to formulate 2step-by-step instructions, or algorithms, to 3solve problems. 1We also learned about logic patterns and 2data patterns. 1This is where the rubber meets the road! 1If we have correctly defined our problem, modeled 2it, and generated the algorithm, the problem is 3essentially solved. All that remains is to 4translate our solution, line by line, into the 5grammar and syntax of whatever software package 6we are using. 1In this lesson we worked through the the defining, 2modeling, formulating, and computing PROCESS 3for actual problems. 1We emphasized process because the idea is to show 2how, in problem solving, we often head down wrong 3paths, have to redefine our terms, develop new 4models, and rewrite our solutions. 1This is not wrong; it's reality. dummy 9 Do you require a database product? 9 Is this database for business use? 9 Will you need to exchange 10 information with other programs, 11 such as spreadsheets? 9 Will people on different 10 computers need to share the 11 information at the same time? 9 Do you require a spreadsheet 10 product? 9 Is this for business use? 9 Will you be working with large 10 spreadsheets (i.e. greater than 11 about 100 rows by 100 columns)? 9 Is it important that you be able 10 to present your information 11 graphically? 9 Will you need to exchange 10 information with other programs, 11 such as databases? 9 Do you require a word processing 10 product? 9 Is this for business use? 9 Do you need to send the same 10 document to many people (form 11 letters, promotional mailings, 12 Christmas letters, etc.)? 9 Do you need to produce specialized 10 documents, such as legal documents? 9 Will you need to read and write 10 documents compatible with other 11 word processing packages? 9 Do you require an accounting 10 system? 9 Do you require a desktop 10 publishing product? 9 Will you be inserting a lot of 10 graphics into your documents? 9 Is this for professional use? 9 Do you require a graphics/art 10 product? 9 Will you use this primarily to 10 produce charts and graphs? 9 There are many types of personal 10 information manager packages to 11 help you organize various aspects 12 of you life. Would you like more 13 information about this type of 14 software on your printout? 9 Would you like to use your 10 computer to bank at home? 9 Would you like to use your 10 computer to make travel 11 reservations? 9 Would you like to be able to 10 shop using your computer? 9 Would you like to have access 10 to research information with 11 your computer? 9 Would you like to participate 10 in electronic conferences with 11 your computer? 9 Would you like to send and 10 receive electronic mail with 11 your computer? 9 Would you like to have access 10 to news, weather, and sports 11 information with your computer? 9 Would you like to receive hardware 10 and software support over the 11 phone, using your computer? 9 Do you require a product to help 10 with home budgeting and income tax 11 preparation? 9 Do you require investment 10 or financial management 11 software? 9 Do you require sales management 10 software? 9 Would you like to use your 10 computer for education? 9 Do you require property management 10 software? 9 Do you require professional 10 office management software? 11 (This includes physicians, 12 dentists, lawyers, etc.) 9 Do you require a CADD system? 10 (Computer Assisted Drafting 11 and Design) 9 Press "P" to get a printed summary 10 of your software and hardware 11 needs. 99