Hard maths riddles: Card games
A small number of cards has been lost from a complete pack. If I deal among four people, three cards remain. If I deal among three people, two remain and if I deal among five people, two cards remain. How many cards are there?
This one is pretty tricky, but the answer is: There are 47 cards. To get the answer, you need to know that there are 52 cards in a pack. Then, find the multiples of four, three, and five closest to that number, and see if any of them are the same. For example, you can deal 42, 44, and 48 cards amongst four people, which would mean 9, 5, or 1 cards is missing (with three remaining). However, the only one that works for multiples of three and five people is when five cards are missing, which gives us a total of 47 cards.
Hard maths riddles: Knight moves
I have a calculator that can display ten digits. How many different ten-digit numbers can I type using just the 0-9 keys once each, and moving from one keypress to the next using the knight’s move in chess? (In chess, the knight moves in an L shape: one square up and two across, two squares down and one across, two squares up and one across, and other like combinations.)
You can form the numbers 5034927618 and 5038167294. You can also form their reverses: 8167294305 and 4927618305. Hence four different numbers can be made. The key point is to realize that the number must start or end on the “5” key, followed/preceded by the ‘0’ key, otherwise, there is no way of using all ten keys during the route.
Hard maths riddles: Three’s company
You know 2 + 2 comes to the same as 2 x 2. Now find a set of three different whole numbers whose sum is equal to their total when multiplied.
The three different whole numbers whose sum is equal to their total when multiplied are 1, 2, and 3.