Simpletonia had an army at last. Ed, the Big Boss, was thrilled and delighted. Jo, the Other Boss, was also thrilled and delighted. Di, Su, Al, Mo, Sy... everybody was overjoyed that now they had a fighting force just like all the other countries. They could participate in the arms race since they had two soldiers with two arms apiece. Estimates of the total number of arms ran as high as eight among the young and excitable before sober thought prevailed and fixed the official count at four.
The Simpletonians could not wait to show off their military might. Invitations were written and in due course an Honoured Visitor from the nearby country of Yonder came to view the marvel. Big Boss Ed greeted him warmly and led him to the turnip field that doubled as a parade ground. There stood the Simpletonian army in all their might. Both of them. There were only two citizens capable of simultaneously counting ("hut! two, three, four") and walking without falling down: twin brothers, men of resource and sagacity, named Newton and Pascal. These, Big Boss Ed informed the Honoured Visitor, were not their birth names but noms de guerre adopted both out of respect for the two famous mathemeticians and to show off the twins' superior prowess in the field of orthography. But it was time for the manoeuvres to begin!
Pascal and Newton marched down the field, duly counting out the pace for each other. Pascal ordered Newton to stand at ease, which he did to perfection. Newton ordered Pascal to form up in a line and, as far as anyone was able to determine, Pascal did so. The best was still to come.
Big Boss Ed explained that the twins had devised an Unbreakable Code to protect against the possibility of espionage.
"Indeed," said the Honoured Visitor. "How does it work, if I may ask?"
The Simpletonians were bursting with impatience to demonstrate.
"Pascal will call out a challenge," said Ed. "If Newton's answer is right, Pascal will know that he is not a spy. But the answer is wrong..." Ed shook his head gravely to disguise the fact that the Simpletonians had not yet considered how to respond to this eventuality.
Luckily, this awkward moment was interrupted by the beginning of the demonstration.
"One!" Shouted Pascal.
After a moment's pause, Newton replied, "One!" Both brothers made a "thumbs up" sign to show that the response was correct.
The Honoured Visitor appeared puzzled. "So, the purpose of this code is so that Pascal can recognize his twin brother Newton?"
Ed nodded happily. The Honoured Visitor appeared to have grasped the essentials of the Simpletonian security system remarkably quickly. "And it works the other way too!"
With this prompting Newton shouted: "Two!"
Pascal replied: "Two!" Again, they both gave the thumbs up.
"So, each soldier has a password?" Asked the Honoured Visitor.
"No," said Ed. "This is the best part of all! They have a secret way to figure out the answer to any challenge. The secret system works for any number. All nine of them!" This was an allusion to the fact that since Old Ab had lost a thumb in a farming accident, the rest of them had decided to forego the use of the number ten out of respect for his disability.
"Three!" Shouted Pascal.
"Three!" Replied Newton.
"I believe I might see a pattern here," said the Honoured Visitor.
"Four!" Shouted Newton.
"Two!" Replied Pascal.
The Honoured Visitor thought for a minute, then smiled. He was kind enough not to reveal that he had broken the Unbreakable Code.
Using the clues given above, can you break the Unbreakable Code and determine the four remaining responses?