23. The birth date of Albert Einstein is 14 March 1879. If we denote Monday by 1, Tuesday by 2, Wednesday by 3, Thursday by 4, Friday by 5, Saturday by 6 and Sunday by 7, which day of the week was Albert Einstein born? Give your answer as an integer from 1 to 7 .
23. Ans: 5

Our reference day is today, 31-5-2006, Wednesday. We shall first count the number of days $D$ from 15-5-1879 to 31-5-2006. The number of leap years between 1879 and 2005 is
$$
\left(\left\lfloor\frac{2005}{4}\right\rfloor-\left\lfloor\frac{1879}{4}\right\rfloor\right)-\left(\left\lfloor\frac{2005}{100}\right\rfloor-\left\lfloor\frac{1879}{100}\right\rfloor\right)+\left(\left\lfloor\frac{2005}{400}\right\rfloor-\left\lfloor\frac{1879}{400}\right\rfloor\right)=31 .
$$

From 1-1-1880 to 31-12-2005 there are 2005-1879 $=126$ years, of which 31 are leap years. Thus $D=95 \times 365+31 \times 366+(365-31-28-14)+(31+28+31+30+31)=46464$. Since 46464 leaves a remainder of 5 when divided by 7, Albert Einstein was born on Friday. The answer is 5 .