The Case with Nine Solutions

The fog was as thick as ever, and he had some difficulty in detecting even the breaks at the edge of the pavement which indicated the positions of house-gates. The walls of the gardens were concealed behind the climbing curtain of vapour. He counted seven entrances and was well on the way to the next when suddenly the roar of a horn made him lift his eyes to the spaces ahead; two golden discs shone almost upon him and only a wild wrench at the wheel saved him from a collision as the strange car swept past on the wrong side.

“Damn their eyes!” he grumbled to himself. “People like that should be hanged. No one has a right to go barging along at twenty miles an hour on a night like this, hustling everyone out of their way. And on the wrong side of the road, too.”

In his swerve he had lost touch with the pavement and he now crept back to the left, steering in gently for fear of rubbing his tyres on the kerb. Then he began counting the gates once more.

“Eight⁠ ⁠… Nine⁠ ⁠… Ten⁠ ⁠… Eleven⁠ ⁠… Twelve. It’s the next one.”

He passed the next gate and drew up just beyond it. Then reflecting that it was hardly safe to leave a car on the street in a night like this, he got down from his seat and went across the pavement to open the gate of the short drive leading up to the house. The entrance was clear, however, and he was about to return to his car when a thought struck him and he lit a match to examine the pillar of the gate.

Leading the way, he snapped down the switch at the foot of the staircase; but to Dr. Ringwood’s surprise, no light appeared above. Sir Clinton pulled a flash-lamp from his pocket and hurried towards the next flat; as he rounded the turn of the stair, he gave a muffled exclamation. At the same moment, a high-pitched voice higher up in the house broke into a torrent of aimless talk.

“That girl’s a bit delirious,” Dr. Ringwood diagnosed, as he heard the sound; and he quickened his ascent. But as he reached a little landing and could see ahead of him, he was brought up sharply by the sight which met his eyes. Sir Clinton was bending with his flash-lamp over a huddled mass which lay on the floor at the head of the flight, and a glance showed the doctor that it was the body of the maid who had admitted him to the house on his earlier visit.

“Come here, doctor, and see if anything can be done for her,” Sir Clinton’s voice broke in on his surprise.

He leaped up the intervening steps and stooped in his turn over the body, while Sir Clinton made way for him and kept the flash-lamp playing on the face. Down the well of the stairs came the voice of the delirious patient, sunk now to a querulous drone.

The briefest examination showed that the victim was beyond help.

The Inspector, followed by Dr. Ringwood, climbed through the open casement and stared in astonishment at the sight before them. The place they had entered was evidently one of the sitting-rooms of the bungalow, and the dust-sheets which covered the furniture indicated that the building had been shut up for the winter. In a big armchair, facing them as they entered, sat the body of a girl in evening dress with a cloak around her shoulders. A slight trail of blood had oozed from a wound in her head and marked her shoulder on the right side. On the floor at her feet lay an automatic pistol. One or two small chairs seemed to have been displaced roughly in the room, as though some struggle had taken place; but the attitude of the girl in the chair was perfectly natural. It seemed as though she had sat down merely to rest and death had come upon her without any warning, for her face had no tinge of fear in its expression.

“I wasn’t far out in putting my money on Mr. Justice, Inspector,” Sir Clinton said thoughtfully, as he gazed at the dead girl. “It might have been days before we came across this affair without his help.”

He glanced round the room for a moment, biting his lip as though perplexed by some problem.

Flamborough refrained from interrupting, but gave a nod of agreement.

“Deaths by violence fall under three heads, I think,” the Chief Constable pursued⁠—“accident, suicide, and homicide, including murder. Now at the bungalow you had two people put to death, and in each case the death must have been due to one or other of these three causes. Ever do permutations and combinations at school, Inspector?”

“No, sir,” Flamborough confessed, rather doubtfully.

“Well, taking the possible ways of two people dying one or other of three different deaths, there are nine different arrangements. We’ll write them down.”

He drew a sheet of paper towards him, scribbled on it for a moment or two, and then slid it across the table towards the Inspector. Flamborough bent over and read as follows:

Hassendean

Mrs. Silverdale

1.⁠—Accident

Accident

2.⁠—Suicide

Suicide

3.⁠—Murder

Murder

4.⁠—Accident

Suicide

5.⁠—Suicide

Accident

6.⁠—Accident

Murder

7.⁠—Murder

Accident

8.⁠—Suicide

Murder

9.⁠—Murder

Suicide

“Now, since in that table we’ve got every possible arrangement which theoretically could occur,” Sir Clinton continued, “the truth must lie somewhere within the four corners of it.”

“Yes, somewhere,” said Flamborough in an almost scornful tone.

As he entered Sir Clinton’s office on the following morning, Inspector Flamborough blurted out bad news without any preliminary beating about the bush.

“There’s been another murder, sir,” he announced, with a tinge of what seemed grievance in his tone.

Sir Clinton looked up from the mass of papers upon his desk.

“Who is it, this time?” he demanded curtly.

“It’s that fellow Whalley, sir⁠—the man who seemed to have some information about the bungalow affair.”

The Chief Constable leaned back in his chair and gazed at Flamborough with an expressionless face.

“This is really growing into a wholesale trade,” he said, drily. “Four murders in quick succession, and we’ve nothing to show for it. We can’t go on waiting until all the population of Westerhaven, bar one individual, is exterminated; and then justify ourselves by arresting the sole survivor on suspicion. The public’s getting restive, Inspector. It wants to know what we do for our money, I gather.”

Inspector Flamborough looked resentful.

“The public’ll have to lump it, if it doesn’t like it,” he said crudely. “I’ve done my best. If you think I ought to hand the thing over to someone else, sir, I’ll be only too glad to do so.”

“I’m not criticising you, Inspector,” Sir Clinton reassured him. “Not being a member of the public⁠—for this purpose, at least⁠—I know enough to appreciate your difficulties.