## August 2013

<<July
**August**
September>>

To solve this month's challenge, you can try various types of searches, but a nice and elegant solution is to use the following linear matrix A:

100001101

010001011

001000111

000100001

000010001

and assign each nine-bit vertex v the five-bit value of the result of the matrix multiplication Av.

It is easy to show that the first (v=0) vertex has all 32 types of neighbors. Lets call them v_0, v_1,..., v_31.

From this follows that if we want to go from any vertex w of color c_1 to a neighbor of color c_2, all we need is to take the w xor v_{c_1 xor c_2} vertex.

Don Dodson suggested a nice solution that not only contains the name and date but also the word "IBM" (look down and you'll find it vertically).

PONDERTHISAUG2013BCFJKLXQVWMYZ45

VQMWZY54B3FCKJXLSIUA2G10OPDNREHT

FCB3XLKJMWVQ54ZYDNOPHTREUASI102G

AUIS01G2NDPOTHERWMQV45YZCF3BLXJK

45YZWMQVLXJKCF3B01G2AUISTHERNDPO

HTREDNOP102GUASIXLKJFCB354ZYMWVQ

2G10SIUAREHTOPDNZY54VQMWKJXLB3FC

JKLX3BCFYZ45QVWMERTHPONDG201ISAU

UASI102GDNOPHTREMWVQ54ZYFCB3XLKJ

CF3BLXJKWMQV45YZNDPOTHERAUIS01G2

QVWMYZ453BCFJKLXISAUG201PONDERTH

OPDNREHTSIUA2G10B3FCKJXLVQMWZY54

KJXLB3FCZY54VQMWREHTOPDN2G10SIUA

G201ISAUERTHPONDYZ45QVWMJKLX3BCF

THERNDPO01G2AUISLXJKCF3B45YZWMQV

54ZYMWVQXLKJFCB3102GUASIHTREDNOP

Matej Kollar wrote a nice game that displays the nine-dimens-dimensional cube and helps you color it.

https://github.com/xkollar/PonderGameAugust2013

*If you have any problems you think we might enjoy, please send them in. All replies should be sent to:* ponder@il.ibm.com