MySQL 5.1.61 - Update table based on two seperate tables

I have three tables:

id   name
1    NULL
2    OLED   
3    legion 
4    project100 
5    group3 
6    0  
7    25 

projectID   externalID  projectTypeID   projectDescription 
0           0               5               UNALLOCATED
25          220339          1               OLED

typeID   typeDesc   
1        Playbook Aligned
2        Transactional Project
3        External Programs
4        UPI
5        Unallocated

I am trying to update Table_1. I only want to update rows with a 'name' that is a digit. I know that I can select those by doing:

SELECT `name`
FROM `Table_1`
WHERE `name` REGEXP '^[0-9]*$'

This gives me:


What I want to do now is to update these Table_1 entries based on Table_2 and Table_3. I need to find the row in Table_2 where Table_2.projectID = Then, I need to find the row in Table_3 where Table_3.typeID = Table_2.projectTypeID. Finally, I need to update with Table_3.typeDesc. It's a confusing situation - unfortunately I can't do much to change the way that these tables are set up. Any help is appreciated.


JOIN Table_2 on(Table_2.projectID =
JOIN Table_3 on(Table_3.typeID = Table_2.projectTypeID)
SET = Table_3.typeDesc
WHERE REGEXP '^[0-9]*$';

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