The Mystery Component is an "Light Emitting Diode" or "LED"
The mystery component is a red light-emitting diode. A high-brightness AlGaAs LED will work very well in this application. It will detect a narrow band of red light centered at about 625 nm. In this role it is a spectrally-selective photodiode.
Since 1972 I've tested numerous LEDs, and most work well as spectrally-selective photodiodes that detect wavelengths of light slightly below their emission wavelength. A major exception is white LEDs, which are actually blue LEDs in which the chip is coated with a phosphor that transforms the blue emission into white.
How It Works
Figure 2 shows the circuit with the hidden component displayed. The LT1001 is a dual-supply op amp that will not work in this single supply circuit. Nevertheless, the Puzzler circuit does produce an output voltage when illuminated with light having a wavelength near that which would be emitted by the LED in its emission mode. How? The output voltage is the photovoltaic voltage from the LED, and it reaches the output through R1.

Figure 2. The mystery component in Figure 1 is a light-emitting diode (LED). Note that the op amp does nothing in this circuit. The photovoltaic voltage from the LED is simply coupled to the output through R1.
For the circuit to be used in a practical application, the negative 9-volt supply shown in Fig. 3 is required. When the LT1001 is connected to a +/- 9-volt dual supply, light of the proper wavelength (e.g., red for a red LED) striking the LED generates a photocurrent that is amplified by the op amp. Capacitor C1 suppresses oscillation. The output voltage range of the practical circuit in Fig. 3 is much greater than that of the photovoltaic circuit in Fig. 2.

Figure 3. Practical version of the circuit shown in Fig. 2 with a dual-polarity supply.
The LED used in the prototype was a LEDTech Electro UT1813-83 red LED encapsulated in water-clear epoxy (Jameco 1586189). Most other red LEDs will also work, and those encapsulated in clear epoxy will provide more signal. While I used a low noise Linear Technology LT1001CN8 op amp (Jameco part number 239222), most op amps should work for demonstration purposes.
Background
During experiments in college in 1966, I first learned that a pn junction can both emit and detect near-IR. When LEDs were commercialized, I learned that they too, could both emit and detect light. I also found that laser diodes can both emit and detect light.
My first application for LEDs as both detectors and emitters was a variety of lightwave communication systems. Beginning in 1990, I began seriously using LEDs as detectors in a variety of sun photometers that measure haze and the total column amount of water vapor in the atmosphere. My first such instrument has been used to make measurements every day the sun shines since February 4, 1990.
Going Further
Others have also experimented with LEDs as spectrally selective photodiodes. You can find some of their work by entering relevant keywords into www.google.com.
References
Forrest M. Mims III, Light Emitting Diodes, Howard W. Sams & Co., 1973, pp. 118-119.
Ibid., Sun Photometer with Light-Emitting Diodes as Spectrally Selective Detectors, Applied Optics, 31, 33, 6965-6967, 1992.
Ibid., An inexpensive and stable LED Sun photometer for measuring the water vapor column over South Texas from 1990 to 2001, Geophysical Research Letters 29, 20-1 to 20-4, 2002.
Ibid., Five years of photosynthetic radiation measurements using a new kind of LED sensor, Photochemistry and Photobiology 77,30-33, 2003.
Forrest M. Mims III and David R. Brooks, Validation of remote-sensing satellites using inexpensive, ground-based instruments (GLOBE Annual Meeting, July 2002).
About the Author
Forrest M. Mims III has been an electronics and science writer and photographer since 1969. He received an IR 100 Award from Industrial Research Magazine for developing an eyeglass-mounted infrared travel aid for the blind. He received a Rolex Award in 1993 for developing a handheld instrument that measured the ozone layer accurately enough to find an error in a NASA ozone satellite. He was named by Discover Magazine (December 2008) as one of the "50 Best Brains in Science." See his home page and publications here and follow him at Twitter.
