Five friends are standing in a line and facing towards the wall wearing Red, Grey, Yellow, Violet and Black Shoes. The persons wearing Yellow and Red Shoes are not standing at the end position. The person in the middle position is wearing Black shoes and the person with Red Shoes

Question

Five friends are standing in a line and facing towards the wall wearing Red, Grey, Yellow, Violet and Black Shoes. The persons wearing Yellow and Red Shoes are not standing at the end position. The person in the middle position is wearing Black shoes and the person with Red Shoes is not in his left. The person wearing violet shoes is standing on extreme right.

a) Who is on 4th position from right?

b) Who is standing on the extreme left position?

Accepted Answer

> [!TLDR] Five friends wearing Red, Grey, Yellow, Violet and Black shoes stand in the order Grey–Yellow–Black–Red–Violet; the 4th position from the right is Yellow and the extreme left is Grey.

> [!FORMULA] Number the 5 positions 1 (extreme left) to 5 (extreme right); translate each restriction ("not at the end", "not to X's left", etc.) into which colours can/can't occupy which position, and solve by elimination.

1. "The person in the middle position is wearing Black shoes": position 3 $=$ Black.
2. "The person wearing violet shoes is standing on extreme right": position 5 $=$ Violet.
3. "Persons wearing Yellow and Red shoes are not standing at the end positions": Yellow, Red $
otin\{1,5\}$ — combined with position 5 already being Violet, this really restricts them from position 1.
4. Remaining colours to place among positions 1, 2, 4: Red, Grey, Yellow.
5. Since Red and Yellow cannot take position 1 (an end), the only colour left for position 1 is **Grey**: position 1 $=$ Grey.
6. "The person with Red shoes is not in his (the Black-shoe person's) left": relative to position 3 (Black), "left" means positions 1 and 2, so Red $
otin\{1,2\}$; since position 1 is already Grey, this means Red $
e$ position 2, so Red must be at position 4 (the only remaining open end/slot for Red among 2 and 4). …

Shape	Perimeter	Area
Square (side $a$ )	$4a$	$a^2$
Rectangle ( $l \times b$ )	$2(l+b)$	$l \times b$
Triangle (base $b$ , height $h$ )	sum of three sides	$\frac{1}{2} \times b \times h$
Circle (radius $r$ )	$2\pi r$	$\pi r^2$

Shape	Surface Area	Volume
Cube (side $a$ )	$6a^2$	$a^3$
Cuboid ( $l \times b \times h$ )	$2(lb + bh + hl)$	$l \times b \times h$
Cylinder (radius $r$ , height $h$ )	$2\pi r h + 2\pi r^2$	$\pi r^2 h$
Sphere (radius $r$ )	$4\pi r^2$	$\frac{4}{3}\pi r^3$

Concept understanding — Mensuration

What is Mensuration?

The Intuition: Why Do We Need Formulas?

The Two Big Categories

1. 2D Shapes (Plane Figures)

2. 3D Shapes (Solid Figures)

The Precise Statement

The Central Formulas (Your Toolkit)

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