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# Knapsack

##### Age 14 to 16Challenge Level

We had a number of solutions to this problem and I would like to mention Karan of Beecroft Primary school and Ross of the Blue Coat School, who both managed to get the first part right but did not quite get to grips with the second.

Below is a very good solution sent by Andrei of School 205 Bucharest. Well done Andrei.

As in the first case I have to deal with a super increasing series, for each coded number there is only one corresponding letter:

 Code Binary Letter 33 01011 K 18 01110 N 20 00001 A 1 10000 P 31 10011 S 20 00001 A 30 00011 C 33 01011 K

So, the coded word is "knapsack". For, the second part of the problem, I take each number and write it in all the possible combinations, which gives us several letters to chose from:

 Code Sum Binary Letter 1 1 10000 p 5 2+3 01100 l 4+1 10010 r 5 00001 a 14 2+3+4+5 01111 o 4 1+3 10100 t 4 00010 b 5 2+3 01100 l 4+1 10010 r 5 00001 a 8 1+2+5 11001 y 1+3+4 10110 v 3+5 00101 e 10 1+4+5 10011 s 1+2+3+4 11110 - 2+3+5 01101 m 5 2+3 01100 l 4+1 10010 r 5 00001 a 4 1+3 10100 t 4 00010 b 7 1+2+4 11-1- z 3+4 00110 f 2+5 01001 i 9 1+3+5 10101 u 4+5 00011 c

There are many possibilities to make a word. But I need to find one which has sense. The possibilities are written in the following table:

 p l o t l y s l t z u r b r v m r b f c a a e a i

The only solution that I can find is: "problematic".