### Greetings

From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How many such students are there?

### Writ Large

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

### Euromaths

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?

# Largest Number

##### Age 11 to 14Challenge Level

Here are the largest solutions that were sent in.

Matthew from South Farnham School:

4096, by doing 4 to the power 3 to the power 2, which is (4 x 4 x 4) x (4 x 4 x 4) = 64 x 64 = 4096.

Josh from Alameda School:

1 048 576, which is 32 to the power of 4 (32 x 32 x 32 x 32).

Greenford School, Dorset sent in 8 796 093 022 208, which is 2 to the power of 43.

Charlotte, Agnes, Susannah and Miranda from Headington Junior School offered 109 418 000 000 000 000 000, which is about 3 to the power 42.

In fact the exact value of 342 is 109 418 989 131 512 359 209 can you say it aloud easily?