Question 28
Spy 009 enters a secure area locked by a seven-digit code made from digits 2 and 3. There are more 2s than 3s, and the code is divisible by both 3 and 4. The spy must unlock it on the first try or trigger the alarm. Help find the code!
1. List all two-digit numbers formed from digits 2 and 3. Using the test that a number is divisible by 4 exactly when its last two digits form a number divisible by 4, determine the code's last two digits.
2. Suppose the code has m digits 2 and n digits 3. It has seven digits and m>n. What values can m have?
3. Using the test that a number is divisible by 3 exactly when its digit sum is divisible by 3, find m and n.
4. From these results, determine the code that spy 009 needs.
1. List all two-digit numbers formed from digits 2 and 3. Using the test that a number is divisible by 4 exactly when its last two digits form a number divisible by 4, determine the code's last two digits.
2. Suppose the code has m digits 2 and n digits 3. It has seven digits and m>n. What values can m have?
3. Using the test that a number is divisible by 3 exactly when its digit sum is divisible by 3, find m and n.
4. From these results, determine the code that spy 009 needs.