Consider the following sum:

• + 1• + 2• + •3 + •1 = 21•

In the above sum, • stands for

The correct answer is 8.

In this problem, the symbol • represents a single unknown digit that appears in every number in the sum. Our goal is to find which digit, when substituted for •, makes the equation true.

The sum is:

• + 1• + 2• + •3 + •1 = 21•

Let us call the unknown digit d. Now we substitute d for • and expand each number in terms of its place value:

$•=d$

$1��=10+d$

$2•=20+d$

$•3=10d+3$

$•1=10d+1$

And the right-hand side:

$21•=210+d$

Now add the left-hand side together:

$d+(10+d)+(20+d)+(10d+3)+(10d+1)$

Group the constant terms and the terms with d:

Constants: 10 + 20 + 3 + 1 = 34

Terms with d: d + d + d + 10d + 10d = 23d

So the left-hand side simplifies to:

$23d+34$

Set this equal to the right-hand side:

$23d+34=210+d$

Subtract d from both sides:

$22d+34=210$

Subtract 34 from both sides:

$22d=176$

Divide both sides by 22:

$d=\frac{176}{22}=8$

Verification: Substitute • = 8 back into the original sum:
8 + 18 + 28 + 83 + 81 = 218
And 21• = 218 ✓

The equation holds perfectly, confirming that • = 8.