Find a six-digit number containing no zeros and no repeated digits that satisfies the following conditions:
1. The first and fourth digits sum to the last digit, as do the third and fifth digits.
2. The first and second digits when read as a two-digit number equal one quarter the fourth and fifth digits.
3. The last digit is four times the third digit.
If you call the number ABCDEF, then you get the following equations.
1. A + D = F and C + E = F
2. AB = DE / 4
3. F = 4 × C
The only numbers that work for C and E are 2 and 6 or 4 and 8, and in order to make F a single-digit number, we can deduce that C = 2, E = 6 and F = 8.
So far, our number is AB2D68.
We know A + D = 8 so A and D are both odd numbers. The only odd number less than 8 that we can use for D to make one-quarter of two-digit number D6 also be a two-digit number is 7, so D = 7 and A is 1. This makes the two-digit number AB 19.
You have 12 black socks and 12 white socks mixed up in a drawer. You’re up very early and it’s too dark to tell them apart. What’s the smallest number of socks you need to take out (blindly) to be sure of having a matching pair?
Three socks. If the first sock is black, the second one could be black, in which case you have a matching pair. If the second sock is white, the third sock will be either black and match the first sock, or white and match the second sock.
Nipples or teats. Cows have four of them, dogs usually have eight and a human (assuming that’s who’s reading this) has two. Cows milk standing up, dogs often lie down and women usually sit when breastfeeding.
A man wants to get into a night club where the bouncers test each person before they can enter. The man waits and watches.
A woman walks up to the bouncers and the bouncers say 6. The woman replies with 3 and goes in.
A small man walks up and they say 12. The man replies 6 and is admitted.
The first guy thinks he’s figured it out and walks up. They say 4 and the man replies with 2, but they don’t let him in.
