What is the sum of the digits of the decimal form of the number represented by brain teaser 22/29/2024 ![]() how much further can I go without saying, look, $b$ has got to be $4$ that's the only option? Whether M is 58 or 85, the answer to the question is the SAME: 5+813. One repeating digit means multiply by 9, two repeating digits means multiply by 99, three repeating digits means multiply by 999, etc. (1/100) (76+ 0.38383.) Step 3: Multiply and divide by as many 9s as there are repeating digits. ![]() Where $b = 0,1,2,3,4,5$ and I guess at this point we can do trial and error.īut we have $100 121$ so $b \ge 2$ and $b \le 4$ and $b! + 16 \equiv 0 \pmod $ and. We have to play around a bit with the values, but for the DIFFERENCE in the digits to 39, the ONLY values that fit are 8 and 5 (64-25 39). Step 2: split the number into whole number and decimal portions. ![]() If one of the digits is $6$ then $N > 6! = 720$ so one of the digits is at least $7$ which we just showed was impossible.Īlso if all three digits, call them $a,b,c$, are all $ 78$ so $b >4$ but $b \le 5$ so $b=5$ and $N = 255$ but $2! + 5! + 5! = 242$ so $255$ is not factorial. If one of the digits of $N$ is $7$ then $7! > 1000> N$ which is impossible. ![]()
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