### The Best Card Trick?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

### Substitution Cipher

Find the frequency distribution for ordinary English, and use it to help you crack the code.

### Secret Transmissions

How can Agent X transmit data on a faulty line and be sure that her message will get through?

# Substitution Transposed

##### Stage: 3 and 4 Challenge Level:

Well done to Holly from Hymers School who cracked this problem. She described her method as follows:

The way I solved this problem was looking at the frequency graph on the Cipher Toolkit. I realised that it would line up with the normal English letter frequency if every letter was moved three to the right (e.g. h-e, d-a), so I moved them all three to the right and came up with a code, which I then transposed. I discovered the factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228 and 456. The first and last two wouldn't be likely, so I kept trying the different factors until I came up with 19 being the correct number of columns.

Writing the message in a 24 by 19 grid and decoding the Caesar shift of +3 gives:

t e e r g k g t r w i t s s a e d a i

h n t a e s a h b i n e i a t r o i e
e t h i t t r e a t a d n g h e w n n
y o e l t h d y n h n v t e r l s t c
w b y w i e e w c t o i h t o e a a e
e e h a n p n e h h r l e h o c n n a
r g a y g a s r i e d l f a m t d d s
e i d s t n a e l i i a r t w r a e t
n n e e o t n j d r n w o w i i g v h
o w v x m o d u r f a i n a t c o e e
t i e c a m m s e a r t t s h b o r h
r t r e s i a t n t y h d c h e d y o
a h t p k m d o a h r c o a o l d m u
i i h t e e a r n e e o o l t l e o s
l d o a l z m d d r d l r l a s a d e
w o u s y o e i t a b o a e n f l e a
a n g a n o t n h n r u t d d r o r g
y t h m e l u a e d i r i a c e f n e
c s t e a o s r y m c e l h o n w c n
h u a a n g s y l o k d e a l c h o t
i p b n d i a s i t f g d l d h i n s
l p o s c c u u v h r l p l w w t v s
d o u o o a d b e e o a a a a i e e a
r s t f o l s u d r n s s b t n p n y




Reading down the columns gives the plaintext:

theywerenotrailwaychildrentobeginwithidontsupposetheyhadeverthoughta