Terms & Conditions
There are 3 labelled boxes, but each of the labels is on the wrong box.
One box contains just apples, one box contains just bananas and the other contains both apples and bananas.
By just selecting one piece of fruit from one box can you determine the correct labels?
Hint: Try taking one piece out.
Take a piece of fruit from the box labelled apples and bananas.
If an apple is taken, then this box is the apples box (as it can't be the apples/bananas box as all of the boxes are mislabelled). This then means that the bananas box is labelled apples, and the apples/bananas box is labelled bananas. Similarly, if a banana is taken, this box is the banana box, the apples box is labelled bananas and the apples/bananas box is labelled apples.
The day before yesterday, Alan was 27. Next year he will be 30, how?
Hint: When was the information provided?
The information was provided on January 1st.
Alan's birthday is on December 31st. He is now 28, the day before yesterday he was 27 and he will be 29 this year and 30 next year.
What is the only number not found in the Roman numerals system?
Each number in the sequence is a representation of the number 32 in different bases, starting with base 10.
Base 10: 32 = 3 x 10^1 + 2 x 10^0 = 3 x 10 + 2 = 32
Base 9 : 35 = 3 x 9^1 + 5 x 9^0 = 3 x 9 + 5 = 32
Base 8 : 40 = 4 x 8^1 + 0 x 8^0 = 4 x 8 + 0 = 32
Base 7 : 44 = 4 x 7^1 + 4 x 7^0 = 4 x 7 + 4 = 32
Base 6 : 52 = 5 x 6^1 + 2 x 6^0 = 5 x 6 + 2 = 32
Base 5 : 112 = 1 x 5^2 + 1 x 5^1 + 2 x 5^0 = 1 x 25 + 1 x 5 + 2 = 32
Base 4 : 200 = 2 x 4^2 + 0 x 4^1 + 0 x 4^0 = 2 x 16 + 0 + 0 = 32 (as required)