Evaluating The Efficacy And Safety Of Donepezil Hydrochloride (Aricept) In The Treatment Of The Cognitive Dysfunction Exhibited By Children With Down Syndrome, Aged 11 To 17

Inclusion Criteria: 1. Age range: Participants 11 to 17 years of age at the screening visit; weight \>35 kilograms (kg). 2. Sex distribution: both males and females. 3. Vineland-II Adaptive Behavior Scales (VABS-II)/Parent/Caregiver Rating Form (PCRF) receptive sub-domain raw score of \>= 25 and expressive sub-domain raw score of \>= 61. 4. Clinical diagnosis of Down syndrome (DS) - participants may have free trisomy 21, Robertsonian translocations, or mosaic DS. 5. Naive to approved or unapproved cholinesterase inhibitors (Aricept, Exelon, Cognex, Reminyl/Razadyne, metrifonate, physostigmine) is preferred. However, prior use of these medications is allowed, provided that the medication was discontinued at least 3 months prior to screening and that it was not discontinued for lack of tolerability or efficacy or for the sole purpose of enrolling the participant in the study. The exception to this prior use is that participants who participated in the Phase II study E2020-A001-219 (A2501059) are not eligible. 6. Participants residing in the community or in facilities that have consistent and reliable caregivers who can provide efficacy information about the participants. 7. The participants must be expected to complete all procedures scheduled during the Screening and Baseline visits including all efficacy and safety parameters. Participants who are verbal and able to be understood most of the time are preferred, but those who use other forms of communication, signs, symbol boards or devices to supplement his/her communication ability may be enrolled provided they meet the VABS-II/PCRF receptive and expressive score criteria mentioned above. 8. Participants must have a parent, or other reliable caregiver who agrees to accompany the participant to all clinic visits, provide information about the participant as required by the protocol, and ensure compliance with the medication schedule. 9. The parent or caregiver must be a constant and reliable informant with sufficient contact with the participant to have detailed knowledge of the participant's adaptive functioning in order to be able to complete the VABS-II/PCRF accurately. The same individual should complete the form at every visit, if possible. 10. Participants should be in good general health with no medical conditions that are considered both clinically significant and unstable. 11. Clinical laboratory values within normal limits or abnormalities considered not clinically significant by the investigator and sponsor. 12. Participants with stable Type I (insulin-dependent) or Type II diabetes are eligible provided they are monitored regularly prior to and during the study to ensure adequate glucose control. (Adequacy of control is based on the investigator's judgment, but should be guided primarily by a glycosylated hemoglobin \[hemoglobin A1c\] \<8.0 at screening; other information, including records of home monitoring and the screening fasting glucose may support this judgment). 13. Participants with thyroid disease also may be included in the study provided they are euthyroid and stable on treatment for at least 1 month prior to screening. 14. Participants with a history of seizure disorder are allowed provided that they are on stable treatment for at least 3 months and have not had a seizure within the past 6 months. 15. Participants should be independent in ambulation or ambulatory aided (i.e., walker or cane, to wheelchair); vision and hearing (eyeglasses and/or hearing aid permissible) sufficient for achieving VABS-II/PCRF minimum receptive raw scores of \>= 25 and expressive scores of \>= 61 and for cooperating with secondary efficacy evaluations and study examinations. 16. Females who have begun menstruation and are thus of child-bearing potential may be enrolled but must be documented not to be pregnant by serum pregnancy testing at screening. They also must be practicing an effective means of birth control (abstinence, oral contraceptives, hormonal implants in place at least 1 month prior to enrollment, or a double-barrier method), which must be documented, and the participant and caregiver must be counseled in writing of the importance of not becoming pregnant during the trial. A urine pregnancy test will be done at the Week 4 clinic visit and must be negative prior to dispensing any medication; a serum pregnancy test will be repeated at the Week 10 (or Early Termination) clinic visit. Exclusion Criteria: 1. Age range: Participants \<11 or \>17 years at the screening visit. 2. Participants with active or clinically significant conditions that will, in the investigator's judgment, affect absorption, distribution or metabolism of the study medication (e.g., inflammatory bowel disease, gastric or duodenal ulcers or severe lactose intolerance); controlled celiac disease is allowed. 3. Participants with a known hypersensitivity to piperidine derivatives or cholinesterase inhibitors. 4. Participants currently receiving cholinesterase inhibitors or who have received them in the 3 months prior to screening or with prior use \>3 months prior to screening who stopped for lack of efficacy or tolerability or simply to enroll the participant in this study. Also excluded are participants who participated in the Phase II study E2020-A001-219 (A2501059). In addition, participants may not have taken any other investigational medications (including memantine) within 3 months prior to screening. 5. Participants without a reliable parent or caregiver (caregiver responsibilities are described in the Inclusion Criteria above), or with parents or caregivers who are unwilling or unable to complete any of the outcome measures and fulfill the requirements of this study. 6. Participants with clinically significant obstructive pulmonary disease or asthma, untreated or not controlled by treatment within 3 months prior to screening. 7. Participants with recent (\<= 1 year) or ongoing hematologic/oncologic disorders (mild anemia allowed). 8. Evidence of active, clinically significant, and unstable gastrointestinal, renal, hepatic, endocrine or cardiovascular system disease. 9. Participants with a current Diagnostic and Statistical Manual of Mental Disorders (DSM-IV) diagnosis of Major Depressive Disorder (MDD) or any current primary psychiatric diagnosis other than DS (as per DSM-IV). Diagnoses that are secondary, such as attention deficit hyperactivity disorder, are allowed. 10. Any condition which would make the patient or the caregiver, in the opinion of the investigator, unsuitable for the study. Unsuitability includes female participants who have begun menstruation and are thus of child-bearing potential, and who are not practicing an effective means of birth control. Female participants who have begun menstruation and are sexually abstinent or who are practicing another effective means of birth control are not excluded but must be counseled in writing along with their caregiver about the importance of not becoming pregnant during the study and must have a negative pregnancy test at screening and pregnancy testing at Weeks 4 and 10.