Professor Van Dusen has a week to escape from Chisholm Prison.
When two colleagues, Charles Ransome and Alfred Fielding, challenge Professor Van Dusen to prove his theory that logic can overcome any difficulty, the Professor accepts the challenge. Van Dusen asserts that he can escape from any prison cell at any time, wearing just the clothes on his back.
Arrangements are made with prison commissioners for Professor Van Dusen to be imprisoned on Death Row in Cell 13 of Chisholm Prison. The prison officials are bewildered at such an experiment but consent to aid the men.
Meanwhile, the Professor's unflappable confidence irks his two fellow scientists; they can hardly wait for their colleague to be proved wrong and to be brought down a notch or two.
Professor Van Dusen makes three strange requests before he enters his cell. He asks for some tooth powder and some money: a five dollar and two ten dollar bills; he also requests that his shoes be polished. As his two colleagues walk away, Professor Van Dusen asks for the time, to which the warden replies that it is seventeen minutes past eleven. The professor then promptly informs Ransome and Fielding that he will join them in their office at half-past eight, one week from that evening.
On entering his cell, the Professor observes how the rats in his cell enter and exit through some abandoned pipes. Using thread from his socks, he ties a piece of linen and some money to one of the rats. On the linen, he writes a message promising a reward of an extra ten dollars if the founder of the linen brings his findings to Hutchinson Hatch at the Daily American. As luck would have it, a young boy who was playing baseball found the note and brought it to Hatch.
With Hutchinson Hatch's help, Professor Van Dusen is eventually able to acquire some nitric acid by way of the pipes; he uses the acid to cut through the steel bars in the window and door. Eventually, he is able to escape through the window even though it is a tight fit. Professor Van Dusen wins his bet with his colleagues, and they are left with no choice but to admire his singular skills and extraordinary deductions.