## The Ladies from U.N.K.A.L.

**'Mad' Ade Bozzay, courtesy of Braingle.com**on

Published in Brain Teasers

With each arrangement considered identical to its reverse, there are 126 possible arrangements.

FKO are interchangeable, and can be arranged 6 ways. FKO stays together unless N is next to M outside GLM (more on that below).

JH must be together, and J must be at the end, because H is the only other Russian speaker. JH has 2 slots in the above configuration (H next to FKO, with J on the outside).

GLM has 1 slot in the above configuration (G next to FKO, opposite JH).

2[JH]*6[FKO]*1[MLG]=12 arrangements, or 2 mirror groups of 6 arrangements each. Thus, 6 distinct arrangements - 1 for each FKO order.

Keeping the above groups self-contained, N has 5 slots (2 within FKO, 1 between FKO and H, 1 between FKO and G, 1 beside M). That makes 30 arrangements - 5 for each FKO order.

When N is in certain positions, however, the groups can break up. Unless N is next to M outside GLM, GLM can be GML. If N is between FKO and GLM, GLM can scramble, and G can be anywhere touching FKO, except N cannot touch L. When G-[L/M]-N are consecutive in either direction, FKO can straddle that subgroup. That makes 126 arrangements - 21 for each FKO order.

Here are the 21 arrangements, using xxx for the interchangeable FKO.

JHNxxxGLM, JHNxxxGML, JHxNxxGLM, JHxNxxGML

JHxxNxGLM, JHxxNxGML, JHxxxNGLM, JHxxxNGML

JHxxxNMGL, JHxxxNMLG, JHxxNMLGx, JHxNMLGxx

JHNMLGxxx, JHxxxGLMN, JHxxGLMNx, JHxGLMNxx

JHGLMNxxx, JHGxxxNML, JHxGxxNML, JHxxGxNML

JHxxxGNML

*By 'Mad' Ade Bozzay, courtesy of Braingle.com.*