Final answer:
In 'Number the Stars', rabbit blood and powdered cocaine are the two ingredients used on white handkerchiefs to trick Nazi dogs during an escape operation.
Step-by-step explanation:
In Number the Stars, the two ingredients used on the white handkerchiefs are rabbit blood and powdered cocaine. These handkerchiefs were part of a clever plan to deceive the Nazi dogs trained to sniff out people. The smell of the rabbit blood was meant to attract the dogs, while the cocaine would then dull the dogs' sense of smell, preventing them from detecting the hidden Jews being smuggled out of the country.