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Number Theory
Level
3
Let p > 3 be a prime number. How many times will a digit in appear at least if is a 20 digit number.
The answer is 3.
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1 solution
Suppose otherwise, which means every digit from 0-9 each repeat twice. Then the sum of digits will be = 2(0+1+2+3+4+5+6+7+8+9) = 90. 90 is divisible by 3, which can't be since p >3 and p is prime. Thus at least one digit will appear thrice.