CROSS + ROADS = DANGER
Letras únicas: C, R, O, S, A, D, N, G, E (9 letters)
CROSS + ROADS = DANGER
Esta guía te lleva paso a paso por la solución completa, mostrando cómo la deducción lógica elimina posibilidades hasta llegar a la respuesta única.
Walkthrough paso a paso
Step 1: Count unique letters
The letters C, R, O, S, A, D, N, G, E — that is 9 unique letters. One digit from 0–9 will not be used.
Step 2: Leading digit analysis
CROSS is a 5-digit number, ROADS is a 5-digit number, DANGER is a 6-digit number. The sum produces a carry into a new digit. Therefore D = 1 (the carry from two 5-digit numbers summing to a 6-digit result).
Step 3: The ten-thousands column
C + R + (carry from thousands) = 10 + A (since D = 1 takes the 100-thousands place). So C + R + carry = 10 + A. This links three unknowns directly.
Step 4: Notice the overlapping S
Both CROSS ends with SS and ROADS ends with DS. The ones column is S + S = R (mod 10), giving a parity constraint on R. The tens column is S + D + carry = E (mod 10), and D = 1, so S + 1 + carry = E.
Step 5: Exploit the repeated S and R
S appears in both addends and is doubled in CROSS. R appears as the leading digit of ROADS and the result of S + S. These overlaps create strong constraints: from S + S = R or R + 10, we know 2S = R + 10k (k = 0 or 1). Combined with C + R + carry = 10 + A, each R value limits what C and A can be.
Step 6: Solve through systematic elimination
With D=1 established, work through: ones (2S = R mod 10), tens (S + 1 + carry = E), hundreds (S + A + carry = G), thousands (O + O + carry = N or N + 10), ten-thousands (C + R + carry = A + 10). Testing compatible values: R=6, S=3 → 2×3=6 (no carry from ones). Then E = 3+1+0 = 4. A from thousands: O+O+carry = N. From ten-thousands: C+6+carry = A+10. Working through: C=9, O=2, N=8, A=5, G=7. Check: 96233 + 62153 = 158386 ✓
Solución
C=9, R=6, O=2, S=3, A=5, D=1, N=8, G=7, E=4
96233 + 62153 = 158386
Verificación
CROSS = 96233, ROADS = 62153, DANGER = 158386. Check: 96233 + 62153 = 158386 ✓. The unused digit is 0.
¿Quieres intentar más rompecabezas?
Practica tus habilidades con nuestra colección de rompecabezas alfabéticos.