Hans, a philosophy major with a minor in physics, is having an interesting discussion with Ivana, a physics major with a minor in philosophy. Hans says that humans are simply biological machines and therefore a literal physical power output level in watts can be determined for them. In fact, he estimates that the total wattage of all the humans on Earth clearly exceeds the total wattage of all nuclear power plants on Earth. Ivana agrees with all of his wattage numbers and calculations except for one simple factor, which corresponds to a difference in interpretation of how to make the comparison. According to Ivana’s estimate, the nuclear power plants have roughly at least the same, or higher, wattage as humans. How might have Hans and Ivana, respectively, done their estimates? Who do you think is right?
Uranium Enrichment for Peaceful Purposes
In this puzzle, Alireza hired Klaus to connect 1,500 centrifuges together to enrich his 100,000 kg of natural uranium. The natural uranium was 0.7% U235 by weight, with the remainder being U238. The goal was to produce within 60 days an overall total of approximately 180 kg of uranium that is at least 93 percent U235, which will be used in medical devices. Each centrifuge can process about 200 g of uranium feedstock per hour. Seventy percent of the U235 entering as feedstock into a centrifuge leaves as product and 30 percent ends up as tailings. Thirty percent of the U238 entering as feedstock into a centrifuge leaves as product and 70 percent ends up as tailings.
Bob Conger demonstrated a very efficient way for Klaus to connect the centrifuges together. When centrifuges are connected sequentially, with the product of one used as the feedstock for the next, the tailing output of the second centrifuge has the same level of enrichment as the feedstock that is input to the first one. (If X is the fraction of U235 in the feedstock of the first centrifuge, then the tailings of the second are X (70%)(30%)/(X (70%)(30%)+(1-X) (70%)(30%)) = X fraction U235.) The centrifuges can be sequentially connected together in nine levels. Level 1 receives as feedstock natural uranium and the tailings from Level 2; Level 2 receives as feedstock the product of Level 1 and the tailings from Level 3; etc. The tailings from Level 1 are discarded and the final product from Level 9 is usable, being 93.5% U235.
Since the usable product is output from Level 9 at 500 g/hr, only 360 hours or 15 days are required to get the 180 kg of highly enriched uranium. Since Level 1 requires only 116,940 g/hr of natural uranium, only 42,079 kg out of the available 100,000 kg is needed.
Bob, Klaus and Alireza all take a 45-day vacation, partying at various locations around the world with the proceeds of selling the remaining 57,921 kg of unneeded natural uranium, and they rejoice at the thought of their imminent Nobel Peace Prize.
Solutions were also submitted by Chris Norman.
AR Puzzle Editor Jon Evans is president of Convergent Actuarial Services, Inc. in Delray Beach, Florida.
