The number of the flock was 301. This is found by first taking the least common multiple of 2, 3, 4, 5, 6, which is 60, and then finding the lowest multiple of this, which with 1 added is divisible by 7. This 301 is exactly divisible by 7, but by the smaller numbers there is 1 as remainder.
65.
The rule for determining easily the number of round bullets in a flat pyramid, with a base line of any length, is this:—
Add a half to half the number on the base line, and multiply the result by the number on that line. Thus, if there are twelve bullets as a foundation—
12 + 1⁄2 = 13⁄2; and 13⁄2 × 12⁄1 = 78.
The same result is reached by multiplying the number on the base line by a number larger by one, and then halving the result. Thus—
12 × 13 = 156, 156 ÷ 2 = 78.