TIN + TIN + TIN = PIPE + PIPE, where I = 4. Find the value of TIN.

Concept: In a cryptarithmetic (alphametic) puzzle, each distinct letter stands for one fixed digit (0-9) used consistently everywhere it appears, and different letters must stand for different digits. TIN + TIN + TIN = PIPE + PIPE means 3 x TIN = 2 x PIPE, so the digits of T, I, N, P, E must satisfy this arithmetic identity exactly, with I fixed at 4.

Working it out:

1. Expand place values: TIN = 100T + 10I + N, and PIPE = 1000P + 100I + 10P + E = 1010P + 100I + E (P repeats in the thousands and tens places).

2. 3 x TIN = 2 x PIPE. Substituting I = 4: 3(100T + 40 + N) = 2(1010P + 400 + E), which simplifies to 300T + 3N - 2E = 2020P + 680.

3. TIN is a 3-digit number, so 3 x TIN is at most 3 x 999 = 2997, meaning 2 x PIPE <= 2997, so PIPE <= 1498. A 4-digit number no greater than 1498 must have leading digit P = 1.

4. With P = 1, the equation becomes 300T + 3N - 2E = 2700. Since 3N - 2E can only range from -18 to +27 for single digits N and E, 300T must lie between 2682 and 2727 - the only single digit satisfying this is T = 9, reducing the equation to 3N = 2E.

5. Solve 3N = 2E for digits 0-9 not already used (T = 9, I = 4, P = 1 are taken): the only pair giving distinct, unused digits is N = 2 and E = 3 (3 x 2 = 6 = 2 x 3).

6. So TIN = 942 and PIPE = 1413.

Cross-check: Substituting back: 3 x 942 = 2826 and 2 x 1413 = 2826 - both sides match, and every letter (T = 9, I = 4, N = 2, P = 1, E = 3) maps to a distinct digit, confirming TIN = 942.