Brain-Teaser 15: Bumper’s final ball
From The Sunday Times, 11th June 1961 [link]
It is a lovely evening in August, and the final Test of the 1990 series has reached its climax. The rubber stands at two games each, the last ball of the last over of the match is now to come. Australia are batting and need six runs for victory. Whacker, their wicket-keeper, the last man in, has taken his stand. with his captain’s words ringing in his ears, “Six or bust!”.
Bumper, the England bowler, has just taken the previous two wickets in succession, With a dim opinion of Whacker’s batting, he feels sure that a fast straight one will not only give England the Ashes, but will give him his hat-trick and his seventh wicket of the match.
In a breathless hush he delivers a fast straight one. Striding forward like a Titan, Whacker mows …
The records of this match are scanty. The Australian total in two innings was 490. Except for one man run out in the first innings, their casualties fell to bowlers. The five England bowlers had averages of 14, 20, 25 (Bumper), 33, 43, each with a differing number of wickets.
How many wickets did each take and who won the Ashes?
This is another puzzle that I originally couldn’t find, but with a bit more searching of the archive I was able to unearth it.
This puzzle completes the archive of Teaser puzzles from 1961 (when the first numbered puzzles appeared).
This is the first of the numbered Teaser puzzles set by Charles Skeffington Quin (although it is credited to R. Skeffington Quinn), and was re-published as Brainteaser 1093 on 17th July 1983 to celebrate Mr Skeffington Quin’s 100th birthday.
[teaser15]
S2T2 
Jim Randell 9:24 am on 22 August 2021 Permalink |
I think you need to something about cricket to solve this puzzle. Unfortunately I am not an expert in cricket, but here goes…
We need to know the number of Australian batmen dismissed by the bowlers, in both innings. In the first innings, all 10 of the batsmen will have been dismissed, but one was run out, so only 9 were bowled. In the second innings, if Australia win, only 9 of the batsmen will have been dismissed (and Bumper will have taken 6 wickets), however if Bumper bowls out the last man all 10 of them will have been dismissed (and Bumper will have taken 7 wickets).
So we are interested in the situation where either 18 wickets are taken (Australia win, and Bumper takes 6 wickets) or where 19 wickets are taken (England win, and Bumper takes 7 wickets).
This Python program runs in 55ms.
Run: [ @replit ]
from enigma import (express, all_different, printf) # the averages (which happen to be an increasing sequence) avgs = (14, 20, 25, 33, 43) # how can a total of 490 be achieved using these averages? for (a, b, c, d, e) in express(490, avgs, min_q=1): # each bowler took a different number of wickets if not all_different(a, b, c, d, e): continue # we are interested in totals of 18 or 19 t = a + b + c + d + e if t == 18 and c == 6: win = "Australia" elif t == 19 and c == 7: win = "England" else: continue # output solution (A, B, C, D, E) = (x * y for (x, y) in zip(avgs, (a, b, c, d, e))) printf("{a} for {A}, {b} for {B}, {c} for {C}, {d} for {D}, {e} for {E}; {win} win")Solution: The number of wickets taken by each bowler are: 5, 2, 7 (Bumper), 1, 4. England won.
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