# Deduce Distinct Digits of the Given Fibonacci Sequence- Detail all Steps

$$DEPUS$$

$$SRST$$

$$UDQD$$

$$CTQU$$

$$DTPR$$

$$PQR$$

$$SDE$$

$$VRR$$

$$CVV$$

$$DUU$$

$$QP$$

$$TT$$

$$D=1,C=2,V=3,R=7,E=0,S=6,Q=8,P=9,T=5,U=4$$

Giving:

$$55,89,144,233,377,610,987,1597,2584,4181,6765,10946$$

Logic:

The brackets contain the line (from the bottom) used.

$$D=1$$ as sum of two 2-digit numbers $$\lt200$$ (123). $$C=2$$ by the same argument (234), therefore, because $$U+V$$ doesn't carry, $$V=3$$ (345). We have $$V+R=E$$ next to $$V+R=D=1$$ (456), so $$V+R$$ must carry, and $$D=E+1$$, so $$E=0$$. Also $$V+C+1=S$$ (456), so $$S=6$$. $$Q=R+D=7+1=8$$ (567), and the second line up tells us $$P=Q+1=9$$ (123). $$P+S=DT$$ (678), so $$T=5$$, giving $$U=4$$ (123).

• Got it......... – Uvc Jul 1 at 11:15
• Alternate approach: The first 3-digit numbers all end in a doubled digit? Surely OP wouldn't have used the actual Fibonacci sequence? – Bass Jul 1 at 15:36