I am the owner of a pet store. If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?
If you put one canary in each cage, you have an extra bird without a cage. However, if you put two canaries in each cage then you have two canaries in the first cage, two canaries in the second cage and an extra cage.
Six glasses are all in a row in front of you, the first three are full of grape juice and the last three are empty. Moving only one glass, how can you make all six alternate between full and empty?
A secret lair has a code to only allow members to enter. The person wanting to enter says a random number, then is told a number in response. In order to enter they must say the correct third number. Here are sequences that allowed entrance.
Five because s-e-v-e-n has 5 letters. The first number can be anything, the second number is the number of letters in the first number, and the third number is the number of letters in the second number.
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.