When he finished, the computer showed that only (n-1) numbers were entered, and the average number was 35 and 5 / 7. What is the number entered at the end

When he finished, the computer showed that only (n-1) numbers were entered, and the average number was 35 and 5 / 7. What is the number entered at the end

Analysis: if the sum of N numbers is (n + 1) & _; n / 2, and the average is (n + 1) / 2 without loss, change the average into a fraction of 250 / 7, one less number has little effect on the whole, and the average output is 35 + 5 / 7, then the estimated n is more than 70. Considering that the denominator is 7, that is, n-1 should be a multiple of 7, 71 and 78 are satisfied in the estimation interval
If the average output is 35 + 5 / 7, it is estimated that n is more than 70, so 70 ≤ n-1 ≤ 79,
And the denominator is 7, that is, n-1 is a multiple of 7, so n is 71 or 78
When n = 71, the sum is 2556 and the divisor is 70, it is easy to see that 56 is missing
When n = 78, the sum is 3081 and the divisor is 77. The divisor removes the factor of 7 and the factor of 11. Then the numerator must be a multiple of 11. 11 * 250 = 2750. The difference is too big to satisfy. Therefore, n is 70 and the leakage number is 56