### Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?

### Angle Trisection

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

# James's Code Challenge

##### Age 7 to 18Challenge Level

The February 2012 problems are all on the theme of codes and codebreaking, in celebration of Alan Turing's centenary.

Instead of featuring a game this month, we have invited James Grime of the Enigma Project to create a code challenge.

You can watch the video here or visit James's YouTube channel and watch it there.

Here is the cipher text:

VA BT LS EG OT XK PB BH CI FV GA YC QG BP UW IH QD OE DI HL CQ YC QG BP EI LZ GA GB IZ PS AZ DQ NI CY UY EA AI UA BF BV OV QA ZS DP QD PG QM PS WL QY DH BD TL VZ PL LW AH GZ BP IM NI KP DZ QU DH FP CI FV RT SB BP BV XO BE BQ PG KO GE IK KO NA OS DG DG DA OX PO GE LZ GA OP FL WU PU UT WF BV IC HF EQ SP NA UX DC BV

Here is the crib:

"EXTRA LARGE FRENCH FRIES"

James has now produced a video solution to his code challenge.

You can read a detailed explanation on James's website here.