Permutations + divisibility - math problems

Number of problems found: 5

• Three numbers
We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers?
• Inverted nine
In the hotel Inverted Nine, each hotel room number is divisible by 6. How many rooms can we count with the three-digit number registered by digits 1,8,7,4,9?
• Digit sum
How many are three-digit numbers that have a digit sum of 6?
• Permutations
How many 4-digit numbers can be composed of numbers 1,2,3,4,5,6,7 if: and the digits must not be repeated in the number b, the number should be divisible by five, and the numbers must not be repeated c, digits can be repeated
• Rectangles
How many rectangles with area 8713 cm2 whose sides are natural numbers are?

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