An expression that equals 377 and contains a multiple of 9 but no 2 or 5
To find an expression that equals 377 and contains a multiple of 9 but no 2 or 5, we need to break down the problem into smaller steps:
Step 1: Find a multiple of 9 that does not contain any 2 or 5.
We know that the sum of the digits of any multiple of 9 is also a multiple of 9. Starting with the smallest multiple of 9 (9 itself), we can add multiples of 9 until we find one that does not contain any 2 or 5. Let's go through the numbers:
9: Contains a 9, which is fine since it is divisible by 9, but it also contains a 2.
18: Contains an 8, which is fine since it is divisible by 9, but it also contains a 2.
27: Contains a 7, which is fine since it is divisible by 9, and does not contain any 2 or 5. We can use this number.
Step 2: Construct an expression that equals 377 using the number found in step 1.
We have the number 27, which is a multiple of 9 but does not contain any 2 or 5. To construct an expression that equals 377, we can use basic arithmetic operations (+, -, *, /) and combine digits to form numbers. Here's an example expression:
(27 + 13) * 10 + 7 = 377
In this expression, we add 27 with 13 to get 40, then multiply it by 10 to get 400, and finally add 7 to get 407. This expression equals 377 while meeting the conditions of having a multiple of 9 and not containing any 2 or 5.