Question

In how many combinations, a cricketer can make a century with fours and sixes only?

Answer 1

Hint – In order to get this problem solved we need to count the number of times we can get the sum 100 in multiplying 4 and 6 with different numbers and summing it to get a hundred. The number of times we got 100 in this method is the answer of the question.

Complete step-by-step answer:
The possible combinations are:
First we calculate with the number of 4s the cricketer can hit to get a total of 100.
(25 × 4),
The number of 4s and 6s the cricketer can hit to get a total of 100.
22 fours and 2 sixes will give us 100.
(22 × 4 + 2 × 6),
19 fours and 4 sixes will give us 100
(19 × 4 + 4 × 6),
16 fours and 6 sixes will give us 100
(16 × 4 + 6 × 6),
13 fours and 8 sixes will give us 100
(13 × 4 + 8 × 6),
10 fours and 10 sixes will give us 100
(10 × 4 + 10 × 6),
7 fours and 12 sixes will give us 100
(7 × 4 + 12 × 6),
4 fours and 14 sixes will give us 100
(4 × 4 + 14 × 6),
1 four and 16 sixes will give us 100
(1 × 4 + 16 × 6)
The cricketer cannot hit only 6s and can make an exact 100.
Hence there are a total of 9 combinations.
So, the answer is 9.

Note – In order to get such types of problems correct we need to use calculations so that we can get the value we want following a respective condition. Like here we have used the number of sixes and fours we need to get the sum 100 so we got 9 types of combinations which gives the sum 100 and satisfies our condition also.