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Puzzles

12 December

Mary uses the digits 1, 2, 3, 4, 5, 6 and 7 to make two three-digit numbers and a one-digit number (using each digit exactly once). The sum of her three numbers is 1000.
What is the smallest that the larger of her two three-digit numbers could be?

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4 December

Some numbers can be written as the sum of four consecutive numbers, for example: 142 = 34 + 35 + 36 + 37.
What is the mean of all the three-digit numbers that can be written as the sum of four consecutive numbers?

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3 December

Holly picks the number 513, reverses it to get 315, then adds the two together to make 828.
Ivy picks a three-digit number, reverses it, then adds the two together to make 968. What is the smallest number that Ivy could have started with?

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12 December

Holly picks a three-digit number. She then makes a two-digit number by removing one of the digits. The sum of her two numbers is 309. What was Holly's original three-digit number?

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5 December

The sum of 11 consecutive integers is 2024. What is the smallest of the 11 integers?

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Tags: numbers, sums

3 December

There are 5 ways to write 5 as the sum of positive odd numbers:
How many ways are there to write 14 as the sum of positive odd numbers?

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Tags: numbers, sums

1 December

Eve writes down five different positive integers. The sum of her integers is 16. What is the product of her integers?

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16 December

Some numbers can be written as the sum of two or more consecutive positive integers, for example:
$$7=3+4$$ $$18=5+6+7$$
Some numbers (for example 4) cannot be written as the sum of two or more consecutive positive integers. What is the smallest three-digit number that cannot be written as the sum of two or more consecutive positive integers?

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