
851 P.2d 15 (1993)
Jack Stanley RUDE, Appellant (Defendant),
v.
STATE of Wyoming, Appellee (Plaintiff).
No. 92-76.
Supreme Court of Wyoming.
April 26, 1993.
*16 Micheal K. Shoumaker, Sheridan, for appellant.
Joseph B. Meyer, Atty. Gen., Sylvia L. Hackl, Deputy Atty. Gen., and Barbara L. Boyer, Sr. Asst. Atty. Gen., for appellee.
Before MACY, C.J., and THOMAS, CARDINE, GOLDEN and TAYLOR, JJ.
TAYLOR, Justice.
Appellant, Jack Stanley Rude, appeals from the district court's decision to accept his pleas of guilty to the crimes of first-degree murder and conspiracy to commit first-degree murder. Appellant raises one issue for our review by asking whether an adequate factual basis was established during re-arraignment to sustain his pleas of guilty to the crimes of first-degree murder and conspiracy to commit first-degree murder. We affirm in part and reverse in part.
Mary Elizabeth Rude was found dead in her Cheyenne, Wyoming apartment on the morning of March 20, 1991. She had been shot three times at close range with a small caliber weapon, twice to the head and once to the back. The investigation of the murder centered upon appellant and his son. A complaint was filed on April 12, 1991, leading to the arrest of appellant in Ohio on April 17, 1991. He was extradited to Wyoming and appeared in county court on June 10, 1991. Counsel was appointed to represent appellant and he was bound over to the district court. He was arraigned in district court on August 9, 1991, and the district court entered a plea of not guilty on his behalf.
Appellant was re-arraigned on March 6, 1992, and, pursuant to a plea agreement, pleaded guilty to first-degree murder and conspiracy to commit first-degree murder. In exchange for appellant's guilty pleas, the prosecution agreed to recommend that he be sentenced to life terms for each count, with the terms to run concurrently. The district court accepted the guilty pleas and sentenced appellant to two concurrent life sentences.

I.
Appellant contends that the district court judge did not adequately establish a factual basis for each charge as required by W.R.Cr.P. 15(f) (Rule 11 under the present rules). W.R.Cr.P. 15(f) provided:

Determining accuracy of plea.Notwithstanding the acceptance of a plea of guilty, the court should not enter a judgment upon such plea without making such inquiry as shall satisfy it that there is a factual basis for the plea.
During re-arraignment, after the district court established that the pleas were voluntary and had placed appellant under oath, the following colloquy occurred:
THE COURT: Okay. With regard tolet's go to count two first. I think that might be a little easier to get a factual basis.
What happened on March 19, 1991? First of all, did it happen here in Cheyenne?
THE DEFENDANT: Yes, it did.
THE COURT: What did you do?
THE DEFENDANT: Beth wasmy daughter-in-law was getting in my face and threatening legal action against my son. I was getting very angry. And she stooped down in front of mewas getting cat food or whateverand she turned her head sideways and said, "You're nothing but a"or "He's nothing *17 but a damned liar." That's when I shot her.
* * * * * *
THE COURT: Okay. So, now, you came to Cheyenne then with the pistol, you came with the intent to kill your daughter-in-law, I take it. Is that right?
THE DEFENDANT: Well, it was not a dyed-in-the-wool decision. It was a decision that I think I reached a few seconds before I actually shot her.
* * * * * *
THE COURT: * * * Tell me about the actual shooting. What happened? How many shots did you shoot?
THE DEFENDANT: Well, the first two shots were, I would say, instantaneous, together, and the third shot followed it byI have no concept of timebut some interval of time.
THE COURT: How much interval? What's your best testimony in that regard?
THE DEFENDANT: My guess would be just a few seconds.
The prosecution provided the following additional information:
[PROSECUTOR]: Your Honor, the premeditation, Mr. Rude, I believe, was laying a factual basis for the shot. He described first the first shot to the head of Ms. Rude. I believe we still have shots two and three. There was a pause between the second shot, a pause between the third shot. And I would submit upon completion of that statement, there would be sufficient evidence to support premeditation.
Appellant asserts that the factual basis which was provided to the district court did not establish premeditation, an element of the crime of first-degree murder. Wyo. Stat. § 6-2-101(a) (Cum.Supp.1992) provides:
Whoever purposely and with premeditated malice, or in the perpetration of, or attempt to perpetrate, any sexual assault, arson, robbery, burglary, escape, resisting arrest or kidnapping, kills any human being is guilty of murder in the first degree.
This court has consistently held that no specific period of time is required for premeditation to occur. State v. Riggle, 76 Wyo. 1, 298 P.2d 349 (1956), cert. denied, 352 U.S. 981, 77 S.Ct. 384, 1 L.Ed.2d 366 (1957). We have concluded that premeditation requires only a brief interval between the formation of the intent or design and the commission of the act. Collins v. State, 589 P.2d 1283, 1292 (1979).
The word "premeditated" when used in reference to first-degree murder implies an interval, however brief, between the formation of the intent or design and the commission of the act.
Id. at 1292. Premeditation need not have existed for any given length of time before the act. It is sufficient that premeditation existed at the time of the act, and the intent and the act may be as instantaneous as successive thoughts. Riggle, 298 P.2d at 367; Cloman v. State, 574 P.2d 410, 418 (Wyo.1978). We agree with the definition of premeditation outlined by the Supreme Court of Colorado:
It matters not how short the interval, if it was sufficient for one thought to follow another, and the defendant actually formed the design to kill, and deliberated and premeditated upon such design before firing the fatal shot, this was sufficient to raise the crime to the highest grade known to the law.
Sandoval v. People, 117 Colo. 588, 192 P.2d 423, 424-25 (1948). See also Young v. State, 849 P.2d 754 (Wyo.1993).
We have held that, when a conviction for first-degree murder is reviewed on appeal, "[d]eliberation and premeditation as the basis for conviction of murder may be inferred from the facts and circumstances surrounding the killing." Buckles v. State, 500 P.2d 518, 521 (Wyo.), cert. denied, 409 U.S. 1026, 93 S.Ct. 475, 34 L.Ed.2d 320 (1972). While Buckles involved a jury's finding of deliberation and premeditation, we hold that this same rule applies to a judge's determination of the factual basis for a plea of guilty to first-degree murder.
*18 We find support for this rule in the plain language of W.R.Cr.P. 15(f) (Rule 11 under the present rules). The rule requires the court to satisfy itself that a factual basis exists for the guilty plea before accepting such plea. The rule does not mandate that the factual basis be established solely from the defendant's admissions.
In their treatise on criminal procedure, LaFave and Israel outline the following purposes of inquiry into the factual basis:
Most importantly, it should protect a defendant who is in the position of pleading voluntarily with an understanding of the nature of the charge but without realizing that his conduct does not actually fall within the charge. * * * In addition, the inquiry into the factual basis of the plea provides the court with a better assessment of defendant's competency and willingness to plead guilty and his understanding of the charges, increases the visibility of charge reduction practices, provides a more adequate record and thus minimizes the likelihood of the plea being successfully challenged later, and aids correctional agencies in the performance of their functions.
Wayne R. LaFave & Jerold H. Israel, Criminal Procedure 938 (2d ed.1992). These purposes are served if the record discloses a factual basis composed of the defendant's testimony and admissions and/or the state's presentation of evidence. The trial judge may properly draw inferences from the defendant's admissions or the evidence presented by the state to satisfy all elements of the crime to which the defendant is pleading guilty.
We find further support for a rule allowing the trial judge to infer the elements of first-degree murder from the facts and circumstances surrounding the killing in North Carolina v. Alford, 400 U.S. 25, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970). In that case, the defendant, indicted for first-degree murder, pleaded guilty to second-degree murder, but then testified he had not committed the murder and was pleading guilty to avoid the risk of the death penalty. Id. at 25, 91 S.Ct. at 162-63. However, because the defendant persisted in his guilty plea and because the state presented evidence indicating the defendant had taken a gun from his house with the stated intention of killing the victim and had later returned declaring he had carried out the killing, the judge accepted his plea. Id. The United States Supreme Court upheld the plea, reasoning that:
[W]hile most pleas of guilty consist of both a waiver of trial and an express admission of guilt, the latter element is not a constitutional requisite to the imposition of criminal penalty. An individual accused of crime may voluntarily, knowingly, and understandingly consent to the imposition of a prison sentence even if he is unwilling or unable to admit his participation in the acts constituting the crime.
* * * When [defendant's] plea is viewed in light of the evidence against him, which substantially negated his claim of innocence and which further provided a means by which the judge could test whether the plea was being intelligently entered * * *, its validity cannot be seriously questioned. In view of the strong factual basis for the plea demonstrated by the State and [defendant's] clearly expressed desire to enter it despite his professed belief in his innocence, we hold that the trial judge did not commit constitutional error in accepting it.
Id. at 36-38, 91 S.Ct. at 167-68 (emphasis added).
Appellant's testimony, together with the offer of proof submitted by the prosecution, provided a sufficient factual basis to support the element of premeditation. Appellant admitted purchasing an airline ticket under an assumed name, concealing a disassembled gun in his baggage, stopping at a rest area to assemble the gun and, finally, traveling to the victim's home and shooting her three times. We find ample evidence from which the district court judge could infer deliberation and premeditation.
We find further evidence supporting the district court judge's inference of deliberation and premeditation in the passage of time between the second and third shots *19 fired by appellant. As we noted above, premeditation requires only a brief interval between the formation of the intent or design and the commission of the act. The State presented evidence, which appellant acknowledged and could not deny, establishing that approximately one minute passed between the second and third shots, that the victim had been moved prior to the third shot and that she was still alive prior to the third shot. The district court judge clearly based his acceptance of appellant's plea of guilty to first-degree murder on an adequate factual basis.
We affirm the district court's decision to accept appellant's plea of guilty to the charge of first-degree murder.

II.
Appellant also entered a plea of guilty to the charge of conspiracy to commit first-degree murder. The district court, in its preliminary remarks to appellant, quoted Bigelow v. State, 768 P.2d 558, 561 (Wyo.1989); Burke v. State, 746 P.2d 852, 855 (Wyo.1987); and W. LaFave & A. Scott, Criminal Law, § 61 at 460-61 (1972) in defining the elements of conspiracy, and said:
"A conspiracy is an agreement between two or more persons to do an unlawful act. The crime of conspiracy is complete when an agreement has been made and overt acts performed to further the unlawful design."
* * * * * *
"One might suppose that the agreement necessary for conspiracy is essentially like the agreement or `meeting of the minds' which is critical to a contract, but this is not the case. A mere tacit understanding will suffice, and there need not be any written statement or even a speaking of words which expressly communicates agreement."
(Emphasis added.)
The plea agreement provided:
The Defendant, Jack Stanley Rude, in conjunction with and with the advice and counsel of his attorneys formally offers to enter pleas of guilty to one count of first degree murder and to conspiracy to commit first degree murder.
The Defendant further offers to set a factual basis for the charge of first degree murder in that he shot Mary Elizabeth Rude three times and that he deliberated for a time between the first and second shots.
The Defendant also agrees to admit that he knew his son, Robert, wanted Mary Elizabeth Rude dead and that he then killed her. Further, the Defendant would not contest or dispute any of the evidence that the state would proffer in support of the charge of conspiracy.
The Defendant understands that in return for his pleas of guilty the state would recommend that he be sentenced to life terms for each count, said terms to run concurrently.
The Defendant further states that this offer is made voluntarily and intelligently after consultation and advice from competent counsel. The Defendant states that this offer represents an intelligent choice among the alternatives which have been explained and that the Defendant is satisfied with counsels['] representation and that the plea is not coerced.
Appellant's factual basis to the conspiracy charge was memorialized on the record by the following exchange between the district court and appellant:
THE COURT: Well, let me go back a minute. Let's go to count one. It says there was a conspiracy. Was there a conspiracy between you and your son?
THE DEFENDANT: I understood from overhearing statements from him that he wanted her dead.
THE COURT: When did you hear these statements?
THE DEFENDANT: Well, many times over the previous, I'd say, two months.
THE COURT: Very well. And so based on your son's statements to you, what did you do?
THE DEFENDANT: Well, I took it upon myself to come out here.
THE COURT: So did you leave Ohio?
THE DEFENDANT: Yes.

*20 THE COURT: Did you purchase an airline ticket?
THE DEFENDANT: Yes, I did.
THE COURT: With United Airlines?
THE DEFENDANT: I don't even remember the airlines.
THE COURT: Did you use an assumed name?
THE DEFENDANT: Yes, I did.
THE COURT: And did you take a pistol with you?
THE DEFENDANT: Yes, I did.
THE COURT: How did you move the pistol through the metal detector?
THE DEFENDANT: I didn't.
THE COURT: What happened?
THE DEFENDANT: The previous day I disassembled the pistol and put it in a tool box, and put the tool box in a duffle bag which I carried out to checked baggage.
THE COURT: Well, let's see, the pistol was in a tool box?
THE DEFENDANT: It was checked baggage. I did not carry it with me.
THE COURT: Okay. I see. So you checked it on the plane. It was disassembled.
THE DEFENDANT: Right.
The prosecution did not produce any further evidence on the conspiracy charge. We agree with appellant that the district court failed to establish an adequate factual basis to support appellant's plea of guilty to the conspiracy charge.
One person cannot by himself conspire. It takes at least 2 persons to conspire. To conspire is to agree to share an unlawful purpose. Two people may share an unlawful purpose without entering a formal or written agreement. It is sufficient if their agreement is shown by conduct, by a wink or a nod, by a silent understanding to share a purpose to violate the law.
United States v. Palladino, 203 F.Supp. 35, 37 (D.Mass.1962).
From the record before us, we can find no evidence that an agreement, tacit, oral or otherwise, was ever established. The record discloses only that appellant overheard statements by his son that he wished the victim was dead. From this we are unable to discern any actual agreement between appellant and his son. Evidence showing a person overheard another person's desires and acted on those desires, without more, will not suffice to prove an understanding between those persons. Without evidence of an agreement, the district court could not properly accept a plea of guilty to the charge of conspiracy.
We reverse the district court's decision to accept appellant's plea of guilty to the conspiracy charge and remand the case to allow appellant to replead to the conspiracy charge and for further proceedings in conformity with this opinion.
