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#66 Easy times?

Set by Phil Lloyd

If you start with the number 185 and move the first digit to the end, you get 851. You get the same result when you multiply 185 by 4.6.

In a similar fashion, the number 15 can be multiplied by a number between 3 and 4 to move its first digit to the end. What number do you need to multiply by?

Can you find a 3-digit number, where the first digit is 1, that must be multiplied by 2.6 to achieve the same effect?

How about a 5-digit number that is multiplied by 1.8? Or a 9-digit number that that is multiplied by 1.9? In each case, consider only numbers where the first digit is 1.

Solution next week

#65 Prime magic squares

Solution

These are the completed squares. For the second one, you may have a rearrangement, like a rotation or reflection. The second square鈥檚 magic constant is 177, which can also be found by adding all the numbers and dividing by 3.