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#54 New year, new numbers

Set by Katie Steckles

Using the numbers 2, 0, 2 and 5 exactly once each, and the operations of addition, subtraction, multiplication and division (and as many brackets as you need), find a way to make each of the totals 1-10.

If you are also allowed to raise one number to the power of another, join digits into two-digit numbers before calculation and use the factorial operator (n! is the product of all the numbers from 1 to n, and 0! is defined as 1), can you make all the numbers up to 30?

For an additional constraint, can you find a way to write each calculation while keeping the numbers in the order 2, 0, 2, 5?

Solution next week

#53 Dividing digits

Solution

We can add a 6 to get 1236, which is divisible by 4.

We can add a 5 to the end to get 12365, which is divisible by 5, then a 4 to get 123654, which is divisible by 6. But then we are stuck, as none of the remaining digits, 7, 8, 9, 0, gives a multiple of 7 when added to the end.

Using the digits 0-9 once each in the order 3816547290 gives a number that is divisible by 10, 381654729 is divisible by 9, 38165472 is divisible by 8, and so on.