october2013 47 © 2013 The Royal Statistical Society Tootsie Pops How many licks to the chocolate? Every American has grown up with the iconic Tootsie Pop commercial of the little boy trying to find the answer to the question “How many licks to the centre of a Tootsie Pop?”. For those from other cultures, here’s a quick recap. Little Boy: “Mr. Owl, how many licks does it take to get to the Tootsie Roll centre of a Tootsie Pop?” Mr. Owl: “Let’s find out. A one…two-hoo…a three…” (crunch sound effect as the temptation to bite becomes too great). (Narrator): “How many licks does it take to get to the centre of a Tootsie Pop? The world may never know.” The world was left in a haze of unknowing; as with Fermat’s last theorem, it was a question that begged to be answered. The Tootsie Pop problem was not quite as old as Fermat’s (1637 for that one), but the question did start back in 1931 when the Tootsie Pop itself was invented. The question was formalized in 1970 when the iconic Tootsie Pop commercial first aired. For those who have never seen it, of for those who need a nostalgia fix, it is at www.youtube. com/watch?v=K2xMGI-QpZw. In 2008, Tootsie Pop tried to capture the public’s eye by hosting a contest to try to find the number of licks to the centre. The rigorous question has been attempted before by various universities, using various techniques ranging from student lick-ins to mechanical licking ma- chines. The average number of licks ranged from Swarthmore College’s 144 licks (obviously big tongues) to as many as Cambridge’s 3481 licks. Clearly there was considerable variability here, and the question was never answered definitively. Even more important, there has been little or no documentation as to the experimental methods used for determining these historical results. It appears that none of the experiments were published, except, of course, on the somewhat less-than-reliable Internet. I decided to find the number of licks by doing some laboratory experiments that focused on key variables that might be considered important to reaching the centre. My rationale was that lab experiments are cheaper than bribing students to lick, and that I was not at a university wealthy enough to finance me to build a licking machine of sorts. But necessity is the mother of inven- tion: I was able to break down my licking experi- ments, isolating three different variables that I considered would have the greatest effect on the number of licks. My variables were: the force of a lick, the temperature of a person’s tongue, and the pH of a person’s saliva. I simulated these ef- fects in a lab by doing a force test that involved a stir plate and some water. Placing a Tootsie Pop in beaker of water (us- ing 150 ml of water for each test) I was able to change the speed of the stir plate to simulate an increased amount of force. I did several tests at four different speeds and used Minitab on the data. ANOVA and a Tukey post hoc test indicated that force of lick was not likely to affect the number of licks to reach the centre of a normally shaped Tootsie Pop. Repeating the experiment with hotter and cooler water temperatures indicated no differ- ence as long as the temperatures were near that of the human body The significant difference was observed at 97°C; well above – indeed danger- ously above – normal human licking capability. I concluded that for human lickers, their body temperature would not affect the number of licks. My last test was to determine if pH levels and solubility of a person’s saliva might be a deter- mining lick factor. After doing four independent tests that considered normal pH, slightly basic pH, slightly acidic pH and a solubility test I was able to do a final ANOVA and come back with p-value of 0.334 – clearly not significant. This suggested that a person’s pH or the amount of saliva they secrete does not affect the number of licks. I was now able to persuade several mathemat- ics classes to lick some Tootsie Pops for me. My preliminary results meant that I did not have to worry about how acidic a person’s saliva was, nor what their body temperature was, nor how hard they pressed on the lollipop with their tongue. Thus armed, I was confident I had something that would help me find the number of licks to the centre. For consistency, I asked the students to lick on the non-banded side of the Tootsie Pop – the sweet has a thicker ridge that runs longitudinally from its North to its South poles – and to lick only on one side. They could proclaim they had found the centre after they were able to “taste chocolate”. After entering the data, I was able to come up with the following results: • Volunteers, 92 • Mean licks, 356.1 • Lick range, 78–1087 • Inter-quartile range, 219.3–479.8 • Standard deviation, 185.7 Tootsie Pops are lollipops on sticks with a ball of chocolate inside them. How many licks does it take to reach the chocolate? Every American child has wondered. Cory Heid set out to find the answer. Table 1. Previous studies. Number of licks to the centre of a Tootsie Pop Licking machines Licking experiments Purdue University – 364 Swarthmore College – 144 University of Michigan – 411 University of Cambridge – 3481 Harvard University – 2255 Purdue University – 252 Source: http://en.wikipedia.org/wiki/Tootsie_Pops Credit: Gilabrand at en.wikipedia.org