Knapsack

Age 14 to 16

Challenge Level Yellow star

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".

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Knapsack

You may also like

N000ughty Thoughts

Mod 3

Novemberish