Document:

Exhibit 10.5

Crypto 1 Acquisition Corp

1221 Brickell Avenue

Miami, Florida 33131

December 6, 2021

Crypto 1 Sponsor LLC

1221 Brickell Avenue

Miami, Florida 33131

 

Ladies and Gentlemen:

 

This letter will confirm our agreement that, commencing on the date
(the “Effective Date”) that the securities of Crypto 1 Acquisition Corp (the “Company”)
are first listed on the Nasdaq Capital Market and continuing until the earlier of (i) the consummation by the Company of an initial business
combination and (ii) the Company’s liquidation (in each case as described in the Registration Statement on Form S-1 (File No. 333-261051)
filed with the Securities and Exchange Commission for the initial public offering (the “IPO”) of the Company’s
securities) (such earlier date hereinafter referred to as the “Termination Date”), Crypto 1 Sponsor LLC or an
affiliate of Crypto 1 Sponsor LLC (the “Provider”) shall take steps directly or indirectly to make available,
or cause to be made available, to the Company certain office space, secretarial and administrative services as may be reasonably required
by the Company from time to time, situated at 1221 Brickell Avenue, Miami, Florida 33131 (or any successor location of the Provider).
In exchange therefor, the Company shall pay the Provider a sum of $10,000 per month on the Effective Date and continuing monthly thereafter
on the first day of each month until the Termination Date.

 

The Provider hereby (i) agrees that it does not have any right, title,
interest or claim of any kind (a “Claim”) in or to any monies that may be set aside in a trust account established
for the benefit of the public shareholders of the Company and into which substantially all of the proceeds of the Company’s IPO
will be deposited (the “Trust Account”), (ii) irrevocably waives any Claim it presently has or may have in the
future as a result of, or arising out of, this letter agreement, which Claim would reduce, encumber, or otherwise adversely affect the
Trust Account or any monies or other assets in the Trust Account and (iii) agrees that it will not seek recourse against the Trust Account
or any monies or other assets in the Trust Account for any reason whatsoever.

 

The Provider (on behalf of itself and its affiliates) grants, and shall
cause its affiliates to grant, to the Company a non-exclusive, fully paid-up, royalty-free, non-sublicensable and non-transferable limited
license, until the Termination Date, to use and exploit the “Crypto 1” word mark and the Crypto 1 logo solely in connection
with the business of the Company and to hold itself out as “Crypto 1 Acquisition Corp”. Any goodwill accruing from the Company’s
use of the licensed trademarks will inure solely to the Provider and its affiliates.

 

    

     

    

 

This letter agreement constitutes the entire agreement and understanding
of the parties hereto in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among
the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated
hereby.

 

This letter agreement may not be amended, modified or waived as to
any particular provision, except by a written instrument executed by the parties hereto.

 

The parties hereto may not assign this letter agreement and any of
their rights, interests, or obligations hereunder without the consent of the other party; provided that the Provider may assign
this letter agreement to an affiliate without the prior written approval of the Company.

 

This letter agreement shall be governed by, construed in accordance
with, and interpreted pursuant to the laws of the State of New York, without giving effect to its choice of laws principles that will
apply the laws of another jurisdiction.

 

This letter agreement may be executed in one or more counterparts,
each of which shall for all purposes be deemed to be an original but all of which together shall constitute one and the same agreement.
Only one such counterpart signed by the party against whom enforceability is sought needs to be produced to evidence the existence of
this letter agreement. In the event that any signature is delivered by facsimile transmission or any other form of electronic delivery,
such signature shall create a valid and binding obligation of the party executing (or on whose behalf such signature is executed) with
the same force and effect as if such signature page were an original thereof.

 

    2

     

    

 

	 	Sincerely,
	 	 	 
	 	CRYPTO 1 ACQUISITION CORP
	 	 	 
	 	By:	/s/ Michael (Xu) Zhao
	 	Name:	Michael (Xu) Zhao
	 	Title: 	Chief Executive Officer

 

	AGREED AND ACCEPTED BY:	 
	 	 	 
	CRYPTO 1 SPONSOR LLC	 
	 	 	 
	By:	/s/ David Hytha	 
	Name:	David Hytha	 
	Title: 	Managing Member	 

 

[Signature Page to Administrative Services Agreement]Exhibit 10.6

 

PRIVATE
PLACEMENT WARRANT PURCHASE AGREEMENT

 

THIS PRIVATE PLACEMENT
WARRANT PURCHASE AGREEMENT, dated as of December 6, 2021 (as it may from time to time be amended, this “Agreement”),
is entered into by and between Crypto 1 Acquisition Corp, a Cayman Islands exempted company (the “Company”), and Crypto
1 Sponsor LLC, a Delaware limited liability company (the “Purchaser”).

 

WHEREAS, the Company
intends to consummate an initial public offering of the Company’s units (the “Public Offering”), each unit consisting
of one Class A ordinary share of the Company, par value $0.0001 per share (a “Share”), and one-half of one warrant.
Each whole warrant entitles the holder to purchase one Share at an exercise price of $11.50 per Share. The Purchaser has agreed to purchase
an aggregate of 7,400,000 warrants (or up to 8,150,000 warrants if the underwriters in the Public Offering exercise in full their option
to purchase additional units) (the “Private Placement Warrants”), at a price of $1.00 per warrant. Each Private Placement
Warrant entitles the holder to purchase one Share at an exercise price of $11.50 per Share, as set forth in the Company’s Registration
Statement on Form S-1 (File No. 333-261051) (the “Registration Statement”), filed with the U.S. Securities and Exchange
Commission (the “SEC”) under the Securities Act of 1933, as amended (the “Securities Act”).

 

NOW THEREFORE, in consideration
of the mutual promises contained in this Agreement and other good and valuable consideration, the receipt and sufficiency of which are
hereby acknowledged, the parties to this Agreement hereby, intending legally to be bound, agree as follows:

 

AGREEMENT

 

Section 1.              
Authorization, Purchase and Sale; Terms of the Private Placement Warrants.

 

A.               
Authorization of the Private Placement Warrants. The Company has duly authorized the issuance and sale of the Private Placement
Warrants to the Purchaser.

 

B.                
Purchase and Sale of the Private Placement Warrants.

 

(i)                
Simultaneously with the initial closing of the Public Offering or on such earlier time and date as may be mutually agreed by the
Purchaser and the Company (the “Initial Closing Date”), the Company shall issue and sell to the Purchaser, and the
Purchaser shall purchase from the Company, 7,400,000 Private Placement Warrants at a price of $1.00 per warrant (the “Purchase
Price”) for an aggregate purchase price of $7,400,000, which shall be paid by wire transfer of immediately available funds,
or by such other method as may be reasonably acceptable to the Company, deposited into the trust account (“Trust Account”)
at a financial institution to be chosen by the Company, maintained by Continental Stock Transfer & Trust Company, acting as trustee,
at least one (1) business day prior to the date of effectiveness of the Registration Statement. On the Initial Closing Date, upon the
payment by the Purchaser of the Purchase Price, the Company shall deliver to Purchaser a certificate evidencing the Private Placement
Warrants duly registered in the Purchaser’s name or effect such delivery in book-entry form.

 

     

     

    

 

(ii)             
 Simultaneously with any additional closing of the Public Offering in connection with the exercise by the underwriters in the Public
Offering of their option to purchase additional units (an “Option Closing Date,” together with the Initial Closing
Date, the “Closing Dates” and each a “Closing Date”), the Company shall issue and sell to the Purchaser,
and the Purchaser shall purchase from the Company, additional Private Placement Warrants (“Additional Private Placement Warrants”)
at the Purchase Price in such amount as is necessary to maintain funds held in the Trust Account at $10.05 per unit, up to an aggregate
of 750,000 Additional Private Placement Warrants, and simultaneously with such purchase of Additional Private Placement Warrants, as payment
in full for the Additional Private Placement Warrants being purchased hereunder, and at least one (1) business day prior to the closing
of all or any portion of the over-allotment option, Purchaser shall pay $1.00 per Additional Private Placement Warrant, up to an aggregate
amount of $750,000, by wire transfer of immediately available funds, or by such other method as may be reasonably acceptable to the Company,
to the Trust Account,. On any Option Closing Date, upon the payment by the Purchaser of the Purchase Price, the Company shall deliver
to Purchaser a certificate evidencing such additional Private Placement Warrants duly registered in the Purchaser’s name or effect
such delivery in book-entry form. For the avoidance of doubt, an Option Closing Date may occur on the same date as the Initial Closing
Date. The closing of the purchase and sale of each of the Private Placement Warrants and the Additional Private Placement Warrants shall
take place at the offices of Ellenoff Grossman & Schole LLP, 1345 Avenue of the Americas, New York, New York, 10105, or such other
place as may be agreed upon by the parties hereto.

 

C.                
Terms of the Private Placement Warrants.

 

(i)                
Each Private Placement Warrant shall have the terms set forth in a Warrant Agreement to be entered into by the Company and a warrant
agent, in connection with the Public Offering (the “Warrant Agreement”).

 

(ii)             
On or before the Initial Closing Date, the Company shall enter into a registration rights agreement with the Purchaser and certain
other holders of the Class B ordinary shares of the Company, par value $0.0001 per share (the “Registration Rights Agreement”)
pursuant to which the Company will grant certain registration rights to such holders relating to such Class B ordinary shares and
the Private Placement Warrants (including the Shares underlying the Private Placement Warrants).

 

Section 2.              
Representations and Warranties of the Company. As a material inducement to the Purchaser to enter into this Agreement and purchase
the Private Placement Warrants, the Company hereby represents and warrants to the Purchaser (which representations and warranties shall
survive the Closing Dates) that:

 

A.               
Organization and Corporate Power. The Company is a corporation duly organized, validly existing and in good standing as
a Cayman Islands exempted company and is qualified to do business in every jurisdiction in which the failure to so qualify would reasonably
be expected to have a material adverse effect on the financial condition, operating results or assets of the Company. The Company possesses
all requisite corporate power and authority necessary to carry out the transactions contemplated by this Agreement and the Warrant Agreement.

 

    - 2 -

     

    

 

B.                
 Authorization; No Breach.

 

(i)                
The execution, delivery and performance of this Agreement and the Private Placement Warrants have been duly authorized by the Company
as of the Closing Dates. This Agreement constitutes the valid and binding obligation of the Company, enforceable in accordance with its
terms. Upon issuance in accordance with, and payment pursuant to, the terms of the Warrant Agreement and this Agreement, the Private Placement
Warrants will constitute valid and binding obligations of the Company, enforceable in accordance with their terms as of the Closing Dates,
subject to bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating
to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law).

 

(ii)             
The execution and delivery by the Company of this Agreement and the Private Placement Warrants, the issuance and sale of the Private
Placement Warrants, the issuance of the Shares upon exercise of the Private Placement Warrants and the fulfillment of and compliance with
the respective terms hereof and thereof by the Company, do not and will not as of the Closing Dates (a) conflict with or result in
a breach of the terms, conditions or provisions of, (b) constitute a default under, (c) result in the creation of any lien,
security interest, charge or encumbrance upon the Company’s capital stock or assets under, (d) result in a violation of, or
(e) require any authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any court
or administrative or governmental body or agency pursuant to, the Memorandum and Articles of Association of the Company (in effect on
the date hereof or as may be amended prior to completion of the Public Offering, as applicable) or any material law, statute, rule or
regulation to which the Company is subject, or any agreement, order, judgment or decree to which the Company is subject, except for any
filings required after the date hereof under federal or state securities laws.

 

C.                
Title to Securities. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement,
the Shares issuable upon exercise of the Private Placement Warrants will be duly and validly issued, fully paid and nonassessable. Upon
issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, the Purchaser will have good title to
the Private Placement Warrants and the Shares issuable upon exercise of such Private Placement Warrants, free and clear of all liens,
claims and encumbrances of any kind, other than (i) transfer restrictions hereunder and under the other agreements contemplated hereby,
(ii) transfer restrictions under federal and state securities laws, and (iii) liens, claims or encumbrances imposed due to the
actions of the Purchaser.

 

D.               
Governmental Consents. No permit, consent, approval or authorization of, or declaration to or filing with, any governmental
authority is required in connection with the execution, delivery and performance by the Company of this Agreement or the consummation
by the Company of any other transactions contemplated hereby.

 

    - 3 -

     

    

 

Section 3.              
Representations and Warranties of the Purchaser. As a material inducement to the Company to enter into this Agreement and issue
and sell the Private Placement Warrants to the Purchaser, the Purchaser hereby represents and warrants to the Company (which representations
and warranties shall survive the Closing Dates) that:

 

A.               
 Organization and Requisite Authority. The Purchaser possesses all requisite power and authority necessary to carry out
the transactions contemplated by this Agreement.

 

B.                
Authorization; No Breach.

 

(i)                
This Agreement constitutes a valid and binding obligation of the Purchaser, enforceable in accordance with its terms, subject to
bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting
creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law).

 

(ii)             
The execution and delivery by the Purchaser of this Agreement and the fulfillment of and compliance with the terms hereof by the
Purchaser does not and shall not as of the Closing Dates conflict with or result in a breach by the Purchaser of the terms, conditions
or provisions of any agreement, instrument, order, judgment or decree to which the Purchaser is subject.

 

C.                
Investment Representations.

 

(i)                
Pursuant to Section 1 of this Agreement, the Purchaser is acquiring the Private Placement Warrants and, upon exercise of the
Private Placement Warrants, the Shares issuable upon such exercise (collectively, the “Securities”) for the Purchaser’s
own account, for investment purposes only and not with a view towards, or for resale in connection with, any public sale or distribution
thereof.

 

(ii)             
The Purchaser is an “accredited investor” as such term is defined in Rule 501(a)(3) of Regulation D
under the Securities Act, and the Purchaser has not experienced a disqualifying event as enumerated pursuant to Rule 506(d) of
Regulation D under the Securities Act.

 

(iii)           
The Purchaser understands that the Securities are being offered and will be sold to it in reliance on specific exemptions from
the registration requirements of the United States federal and state securities laws and that the Company is relying upon the truth and
accuracy of, and the Purchaser’s compliance with, the representations and warranties of the Purchaser set forth herein in order
to determine the availability of such exemptions and the eligibility of the Purchaser to acquire such Securities.

 

(iv)            
The Purchaser decided to enter into this Agreement not as a result of any general solicitation or general advertising within the
meaning of Rule 502(c) of Regulation D under the Securities Act.

 

(v)              
The Purchaser has been furnished with all materials relating to the business, finances and operations of the Company and materials
relating to the offer and sale of the Securities which have been requested by the Purchaser. The Purchaser has been afforded the opportunity
to ask questions of the executive officers and directors of the Company. The Purchaser understands that its investment in the Securities
involves a high degree of risk and it has sought such accounting, legal and tax advice as it has considered necessary to make an informed
investment decision with respect to the acquisition of the Securities.

 

    - 4 -

     

    

 

(vi)            
 The Purchaser understands that no United States federal or state agency or any other government or governmental agency has passed
on or made any recommendation or endorsement of the Securities or the fairness or suitability of the investment in the Securities by the
Purchaser nor have such authorities passed upon or endorsed the merits of the offering of the Securities.

 

(vii)         
The Purchaser understands that: (a) the Securities have not been and are not being registered under the Securities Act or
any state securities laws, and may not be offered for sale, sold, assigned or transferred unless (1) in a transaction subsequently
registered thereunder or (2) sold in reliance on an exemption therefrom; and (b) except as specifically set forth in the Registration
Rights Agreement, neither the Company nor any other person is under any obligation to register the Securities under the Securities Act
or any state securities laws or to comply with the terms and conditions of any exemption thereunder. In this regard, the Purchaser understands
that the SEC has taken the position that promoters or affiliates of a blank check company and their transferees, both before and after
an initial business combination, are deemed to be “underwriters” under the Securities Act when reselling the securities of
a blank check company. Based on that position, Rule 144 adopted pursuant to the Securities Act would not be available for resale
transactions of the Securities despite technical compliance with the requirements of such Rule, and the Securities can be resold only
through a registered offering or in reliance upon another exemption from the registration requirements of the Securities Act.

 

(viii)       
The Purchaser has such knowledge and experience in financial and business matters, knows of the high degree of risk associated
with investments in the securities of companies in the development stage such as the Company, is capable of evaluating the merits and
risks of an investment in the Securities and is able to bear the economic risk of an investment in the Securities in the amount contemplated
hereunder for an indefinite period of time. The Purchaser has adequate means of providing for its current financial needs and contingencies
and will have no current or anticipated future needs for liquidity which would be jeopardized by the investment in the Securities. The
Purchaser can afford a complete loss of its investment in the Securities.

 

(ix)            
The Purchaser understands that the Private Placement Warrants shall bear the legend substantially in the form set forth in the
Warrant Agreement.

 

Section 4.              
Conditions of the Purchaser’s Obligations. The obligation of the Purchaser to purchase and pay for the Private Placement
Warrants is subject to the fulfillment, on or before the Closing Dates, of each of the following conditions:

 

A.               
Representations and Warranties. The representations and warranties of the Company contained in Section 2 shall be true
and correct at and as of the Closing Dates as though then made.

 

B.                
Performance. The Company shall have performed and complied with all agreements, obligations and conditions contained in
this Agreement that are required to be performed or complied with by it on or before the Closing Dates.

 

C.                 No
Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted,
entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory
organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions
contemplated by this Agreement or the Warrant Agreement.

 

    - 5 -

     

    

 

D.               
Warrant Agreement. The Company shall have entered into a Warrant Agreement with a warrant agent on terms satisfactory to
the Purchaser.

 

Section 5.              
Conditions of the Company’s Obligations. The obligations of the Company to the Purchaser under this Agreement are subject
to the fulfillment, on or before the Closing Dates, of each of the following conditions:

 

A.               
Representations and Warranties. The representations and warranties of the Purchaser contained in Section 3 shall be
true and correct at and as of the Closing Dates as though then made.

 

B.                
Performance. The Purchaser shall have performed and complied with all agreements, obligations and conditions contained in
this Agreement that are required to be performed or complied with by the Purchaser on or before the Closing Dates.

 

C.                
Corporate Consents. The Company shall have obtained the consent of its Board of Directors authorizing the execution, delivery
and performance of this Agreement and the Warrant Agreement and the issuance and sale of the Private Placement Warrants hereunder.

 

D.               
No Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted,
entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization
having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this
Agreement or the Warrant Agreement.

 

E.                
Warrant Agreement. The Company shall have entered into a Warrant Agreement with a warrant agent on terms satisfactory to
the Company.

 

Section 6.              
Termination. This Agreement may be terminated at any time after December 10, 2021 upon the election by either the Company or
the Purchaser upon written notice to the other party if the closing of the Public Offering does not occur prior to such date.

 

Section 7.              
Survival of Representations and Warranties. All of the representations and warranties contained herein shall survive the Closing
Dates.

 

Section 8.              
Definitions. Terms used but not otherwise defined in this Agreement shall have the meaning assigned to such terms in the registration
statement on Form S-1 relating to the Public Offering that the Company has filed with the SEC (the “Registration Statement”),
under the Securities Act.

 

Section 9.              
Miscellaneous.

 

A.                Successors
and Assigns. Except as otherwise expressly provided herein, all covenants and agreements contained in this Agreement by or on
behalf of any of the parties hereto shall bind and inure to the benefit of the respective successors of the parties hereto whether
so expressed or not. Notwithstanding the foregoing or anything to the contrary herein, the parties may not assign this Agreement,
other than assignment by the Purchaser to affiliates thereof (including, without limitation to one or more of its members).

 

    - 6 -

     

    

 

B.                
Severability. Whenever possible, each provision of this Agreement shall be interpreted in such manner as to be effective
and valid under applicable law, but if any provision of this Agreement is held to be prohibited by or invalid under applicable law, such
provision shall be ineffective only to the extent of such prohibition or invalidity, without invalidating the remainder of this Agreement.

 

C.                
Counterparts. This Agreement may be executed simultaneously in two or more counterparts, none of which need contain the
signatures of more than one party, but all such counterparts taken together shall constitute one and the same agreement.

 

D.               
Descriptive Headings; Interpretation. The descriptive headings of this Agreement are inserted for convenience only and do
not constitute a substantive part of this Agreement. The use of the word “including” in this Agreement shall be by way of
example rather than by limitation.

 

E.                
Governing Law. This Agreement shall be deemed to be a contract made under the laws of the State of New York and for all
purposes shall be construed in accordance with the internal laws of the State of New York.

 

F.                 
Amendments. This Agreement may not be amended, modified or waived as to any particular provision, except by a written instrument
executed by all parties hereto.

 

G.               
Trust Waiver. Notwithstanding anything to the contrary herein, the Purchaser hereby waives any and all right, title, interest
or claim of any kind (“Claim”) related to the Private Placement Warrants or this Agreement in or to any distribution
from the Trust Account in which the proceeds of the Public Offering, as described in greater deal in the Registration Statement and the
related prospectus, will be deposited, and hereby agrees not to seek recourse, reimbursement, payment or satisfaction for any Claim against
the Trust Account for any reason whatsoever.

 

[Signature Page Follows]

 

    - 7 -

     

    

 

IN WITNESS WHEREOF,
the parties hereto have executed this Agreement to be effective as of the date first set forth above.

 

	 	COMPANY:
	 	 
	 	CRYPTO 1 ACQUISITION CORP
	 	 
	 	By:	/s/ Michael (Xu) Zhao
	 	Name: Michael (Xu) Zhao
	 	Title: Chief Executive Officer
	 	 	 
	 	PURCHASER:
	 	 
	 	CRYPTO 1 SPONSOR LLC
	 	 
	 	By: 	/s/ David Hytha
	 	Name: David Hytha
	 	Title: Managing Member

 

[Signature Page to Private Placement Warrant Purchase
Agreement]

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00337-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00337-of-00352.parquet"}]]