Lesser Digits
How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
Hiya there!
This is my solution to the question "Lesser Digits" in "The April Six". I sincerely hope that it is good enough to be published on the web page. By the way, that web page is very interesting.
Numbers that do not contain any of the digits 7, 8 and 9
Number that do not contain any of the digits 7, 8 or 9  
1 to 10  7 (1, 2, 3, 4, 5, 6, 10) 
11 to 20  7 
21 to 30  7 
31 to 40  7 
41 to 50  7 
51 to 60  7 
61 to 70  6 
71 to 80  0 
81 to 90  0 
91 to 100  1 
Subtotal: (1 to 100)  7 x 7 = 49 
101 to 200  49 
201 to 300  49 
301 to 400  49 
401 to 500  49 
501 to 600  49 
601 to 700  48 
701 to 800  0 
801 to 900  0 
901 to 1000  1 
Subtotal: (1 to 1000)  49 x 7 =343 
1001 to 2000  343 
2001 to 3000  343 
3001 to 4000  343 
Total: (1 to 4000) 
343 x 4 = 1372

School: RAFFLES GIRLS' PRIMARY SCHOOL
Class: 6i
Nisha Doshi of the Mount School, York, James Page, Jamie Arnall and Jack Adcock of Hethersett High School, and Astee Goh and Teo Yea Tian Raffles Girls' Primary School, Singapore sent good solutions to this and Ian Green , age 13 of Coopers Company and Coburn School, Upminster, Essex came very close. There were many incorrect solutions sent in for this one.