There are 120 different ways of arranging the letters, U, K, M, I and C.

If all of these arrangements are listed in dictionary order, starting with in 1st place CIKMU, what numbered place does UKIMC have the list?

**Answer**: As the selection of neat solutions below show, UKIMC comes in at 112th on the list. Very well done, in order of supplying the correct reply. to: **David Mann**, key account manager, SPC Rubber Compounding, UK; **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **John Bowen**, rubber industry consultant, Bromsgrove, UK; **Stephan** **Paischer**, head of product management special products, Semperit AG Holding, Vienna, Austria;

*Solutions*

*David Mann*

*The group beginning with U is 97 to 120.*

*Then the group beginning UK is 109 to 114, and UKI is 111 to 112, UKIM is therefore 112.*

*Michele Girardi*

*The arrangements that precede UKIMC are :*

*arrangement group quantity
C * * * * 4! = 24
I * * * * 24
K * * * * 24
M * * * * 24
U C * * * 3!= 6
U I * * * 6
U K C * * 2!= 2
U K I C M 1
for a total of 111, so UKIMC is the 112th.*

*For a double check, the arrangements that follow are :
arrangement group quantity
U K M * * 2! = 2
U M * * * 3! = 6*

*indicating the last arrangement as the 120th as known .*

*Andrew Knox*

*Assign numbers to the letters, i.e. C I K M U = 1 2 3 4 5, then it's easy.*

*The first number is then 12345*

*The last number is then 54321*

*There are 6 combinations in the 54... series*

*There are 6 combinations in the 53... series, of which UKIMC (53241) is the third highest, so 8 numbers are higher than 53241. *

*120 - 8 = 112.*

New teaser on Monday