| Neither Ellison's (clue 2), Gates' (4), Icahn's (5), nor Buffett's (6)
order was the 5th and last share purchase, so Schwab's was. By clue 6,
investor Buffett's share purchase came immediately ahead of Michael's,
while by clue 7, Jack called in his order immediately before investor
Icahn did. The only possible commonality between the two clues is if
Jack were Buffett and Michael Icahn. However, by clue 7, then, Michael
Icahn's order would have been for 1,250 more shares than Jack Buffett's,
but by clue 6, Jack Buffett's order would have been for 2,500 more shares
than Michael Icahn's. So, four of the five share purchasers are named
between clues 6 and 7. Since the Ben isn't Buffett (1) and made his
share purchase later in the morning than Icahn did (5), Ben's order
is the fifth to the four in clues 6 and 7. There are three possible
orderings for the five purchases given clues in 5, 6, and 7: 1) Jack's,
Icahn's, Ben's, Buffett's, and Michael's; 2) Jack's, Icahn's, Buffett's,
Michael's, and Ben's; or 3) Buffett's, Michael's, Jack's, Icahn's, and
Ben's. In the first arrangement, Michael would be Schwab, contradicting
clue 3. Trying the second arrangement, Ben would be Schwab. Jack
would be Gates (4), and Michael then Ellison. Since Gates purchased 1,500
fewer shares than Cynthia (4), Cynthia wouldn't be Icahn, who ordered 1,250
more shares than Jack (7). Cynthia would be Buffett and Helen Icahn.
Letting Ellison's number of Oyl Energy shares ordered equal X,
Buffett would have ordered X + 2,500 (6), Helen Icahn 2X (2),
and Jack Gates 2X - 1,250 (7). Jack Gates also would have bought
X + 1,000 (4), so that 2X - 1,250 would equal X + 1,000.
Solving, X would equal 2,250. So, Michael would have bought 2,250,
Cynthia 4,750, Helen 4,500, Jack 3,250, and Ben Schwab (3) 3,000. However,
there would be two differences between numbers of shares purchased of
250--impossible by clue 8. Therefore, arrangement 2) also fails, and
arrangement 3) remains: Buffett's Oyl stock purchase followed in order
by Michael's, Jack's, Icahn's, and Ben Schwab's, which was for 3,000
shares (3). Cynthia isn't Buffet (4); she is Icahn, and the Helen is
Buffett. Since Cynthia Icahn bought 1,250 more shares than Jack (7),
Jack isn't Gates, who ordered 1,500 fewer shares than Cynthia (4). Jack
is Ellison and Michael Gates. Letting the number of shares Jack Ellison
purchased equal X, Cynthia Icahn bought X + 1,250 (7). Helen
Buffett ordered 2X (2), so Michael Gates bought 2X - 2,500 (6).
Michael Gates also ordered X - 250 (4). So, 2X - 2,500 =
X - 250. Solving, X equals 2,250. Thus Jack ordered 2,250,
Cynthia 3,500, Helen 4,500, and Michael 2,000 shares of Oyl Energy stock.
The five investors placed purchase orders with Scott Short-Sellers last
Friday morning as follows:
- 1st - Helen Buffett, 4,500
- 2nd - Michael Gates, 2,000
- 3rd - Jack Ellison, 2,250
- 4th - Cynthia Icahn, 3,500
- 5th - Ben Schwab, 3,000
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