![]() Of course, the line is so long that it circles the earth twice but it is straight nonetheless and solves the puzzle successfully. But what if the box is not the square described by the nine dots but rather, the piece of paper the puzzle is printed on? If we think outside of THAT box, it is possible to solve the puzzle using only one straight line.Įven without manipulating the paper, there is still another way to solve the puzzle using only one straight line. This solution is even further "outside the box" than the first. For those unfamiliar, the most popular solution to the puzzle is depicted below.Ĭlearly, this solution requires one to "think outside" the "box" that is formed by the nine dots but if we are to fully embrace the idea of "outside the box" thinking, why stop there? Here's a way to solve the puzzle using only three straight lines. Though, in a 1959 compendium of Sam Loyd's work, Martin Gardner described this particular puzzle as a "classic geometrical challenge" so the nine dots likely predate Loyd's eggs. The enduring aspect of the puzzle is that it highlights the way our minds tend to impose unnecessary limitations upon methods of attacking problems. The first known publication was in Sam Loyd's classic Cyclopedia of Puzzles, 1914. Whether or not the nine dot problem is in fact the original inspiration for the cliched metaphor, the puzzle itself certainly pre-dates the phrase. The solution requires the functional use of the box which at first, may seem to be included simply to contain the push pins. The challenge is to affix the candle to the wall in such a way that when the candle is lit, the wax will not drip onto the table. CONNECT DOTS WITH 4 LINES FULLIn Duncker's test, participants are presented with a candle, a book of matches and a box full of push pins. The solution requires one to "think outside the box" and while some contend that the nine dot problem served as the inspiration for this popular turn of phrase, others point to a cognitive performance test from 1945 known as Duncker's candle problem. Participants are presented with a set of dots arranged in a 3x3 grid and challenged to connect all nine dots, without lifting their pencil from the paper, using the fewest possible number of straight lines.Ĭopy the simple diagram below onto a piece of paper and give the puzzle a try for yourself before reading any further. CONNECT DOTS WITH 4 LINES SOFTWARELet our drilling software assist you connect more dots.The nine dot problem is a classic lateral thinking exercise that gained widespread popularity in the 1970's and 80's. Connecting dots in drilling engineering reveals the trends of operation date and window of safety to operate. So you have to trust that the dots will somehow connect in your future.”Ĭonnecting dots in our lives gives us confidence to follow our hearts even when it leads us off the well worn path. Steve Jobs once said this in his famous commencement address to Stanford University: “You can’t connect the dots looking forward you can only connect them looking backwards. We call this powerful feature of automatic run on multiple cases “Sensitivity Study”. The following pictures show the impacts of open hole excess on top of cement (TOC) and hydrostatic pressure difference. This process is automated in many of our drilling software models. If we can compile the output from multiple runs of computer model, we can see the trend. Individual case study with one set of input data only tells one story. ![]() You can see from the dots (field measurements) and the lines (model prediction) that the friction factor of 0.32 is a good estimation for slack off operation. The following picture is a screen from TADPRO (torque and drag model). If we can observe hookloads or surface torque for certain operation at various depths, we can calibrate friction factor (back calculation). One of the uncertainties in torque and drag analysis for drilling is the friction factor, because it is dependent on many things such as mud type (oil-based or water-based), pipe moving in casing (steel) or in open hole (rock), cutting concentration, etc. ![]() Looking at dots, we obtain limited information, but more often, we miss the big picture if our vision is restricted to the dots only. Dots are isolated incidents, individual cases, snap shots, discrete numbers, etc. ![]()
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