There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4.
Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a "ping". Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping.
The following additional information is known: 1. B1 and B6 each made a ping on H4, but B5 did not. 2. B4 made a ping on H3, but B1 did not. 3. All balls, except B3, made pings on H1. 4. None of the balls, except B2, made a ping on H2.
Q6
LR - Arrangements TYPE IN THE ANSWER
What was the total number of pings made by B1, B2, and B3?
Answer: 6
A ball pings on a hoop exactly when ball \(\le\) hoop.
Only B2 pings on H2, so B2 \(\le\) H2 < every other ball.
B4 pings on H3 and B4 > H2, so H2 < B4 \(\le\) H3.
B1 does not ping on H3 but pings on H4: H3 < B1 \(\le\) H4.
B5 does not ping on H4 but pings on H1: H4 < B5 \(\le\) H1.
B3 alone fails on H1: H1 < B3.
B6 pings on H4 and H1, not on H2: H2 < B6 \(\le\) H4 (its position relative to H3 is unknown).
Combined chain: B2 \(\le\) H2 < B4 \(\le\) H3 < B1 \(\le\) H4 < B5 \(\le\) H1 < B3, with B6 somewhere between H2 and H4.
Ball
Pings on
Number of pings
B2
H1, H2, H3, H4
4
B4
H1, H3, H4
3
B1
H1, H4
2
B6
H1, H4 and possibly H3
2 or 3
B5
H1
1
B3
none
0
B1 makes 2 pings, B2 makes 4 and B3 makes 0, a total of \(2+4+0 = 6\).
