Solution
Understanding the set -
- There are four institutions having contract with four vendors, from 2010 to 2019.
- contracts were either multi-year contracts running for several consecutive years or single-year contracts
- No institute had more than one contract with the same vendor, but an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes
For eg - there is an institute 'W' and contractor 'A'
so, the point says, W and A cannot have more than one contract,
But, W can have contracts with more then one contractor
and, A can have contract with more then one institute.
- the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes.
=> there were 8 contracts in total, wherein each institute and each vendor had 2 contracts.
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | ||||||||||
| B (7,1) | ||||||||||
| C (3,1) | ||||||||||
| D (4,1) |
Clue 5 says,
There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4-year contract, and A and C had one 3-year contract each. The other four contracts were single-year contracts.
We know, there are 8 contracts
so, this clue gives us details about the time length of these two contracts for each vendor.
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | ||||||||||
| B (7,1) | ||||||||||
| C (3,1) | - | (✓) | ||||||||
| D (4,1) |
Clue 6 says,
Institute C had one or more contracts in 2012 but did not have any contract in 2011.
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | ||||||||||
| B (7,1) | (✓) - 1 | |||||||||
| C (3,1) | - | (✓) | ||||||||
| D (4,1) | - | (✓) - 1 |
Clue 7 says,
Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | ||||||||||
| B (7,1) | (✓) - 1 | |||||||||
| C (3,1) | - | (✓) | ||||||||
| D (4,1) | - | (✓) - 1 |
Clue 1 says,
Vendor Z had at least one contract in every year.
Total number of years = 10 (2010 to 2019)
Therefore, only possibility -
i)7+3 = 10
ii) 7+4 = 11 year contract
and that 7-year contract must be from B.
=> B had a 7 year contract with Z.
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | ||||||||||
| B (7,1) | (✓) - 1 | |||||||||
| C (3,1) | - | (✓) | ||||||||
| D (4,1) | - | (✓) - 1 |
Clue 3 says,
Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012.
Also, according to clue 7, Institutes B and D each had exactly one contract in 2012
=> W has got contracts from A and C
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | X | X | X | |||||||
| B (7,1) | (✓) - 1 | |||||||||
| C (3,1) | - | (✓) | ||||||||
| D (4,1) | - | (✓) - 1 |
Clue 2,
Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that
and from 6 & 7:
C and D didn't have any contract in 2011 and 2010 respectively
=> A should have X as a 3-year contract from 2010-2012.
Now, for 2013-2015 X can't have B for the same.
So, X must have got contracts from either C or D in that period.
Let's divide it into 2 cases -
CASE -1 :
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | X | X | X | |||||||
| B (7,1) | (✓) - 1 | |||||||||
| C (3,1) | - | X | X | X | ||||||
| D (4,1) | - | (✓) - 1 |
X has C as a 3-year contract from 2013-2015
but in this case, D can't have any contract in 2012 so, this case is not valid.
CASE - 2:
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | X | X | X | |||||||
| B (7,1) | Z | Z | Z | Z | Z | Z | Z | |||
| C (3,1) | - | (✓) | Z | Z | Z | |||||
| D (4,1) | - | X | X | X | X |
X has D for a 4-year contract from 2012-2015
and C must have Z for a three-year contract in the period 2017-2019
Such that Z has at least one contract every year
Also, we have found that Z has a 7 year contract with B.
=> Z will have 7 year contract with B from 2010 to 2016.
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | X | X | X, W | - | - | - | - | - | - | - |
| B (7,1) | Z | Z | Z | Z | Z | Z | Z | |||
| C (3,1) | - | - | W | - | - | - | - | Z | Z | Z |
| D (4,1) | - | X | X | X | X |
It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes
=> A hasn't got any contract from 2013-2019 as it has X,
W in the period 2010-2012
and similarly, C shouldn't have any contracts in the years 2010, 2013, 2014, 2015, 2016.
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | X | X | X,W | - | - | - | - | - | - | - |
| B (7,1) | Z, Y | Z | Z | Z | Z | Z | Z | - | - | - |
| C (3,1) | - | - | W | - | - | - | - | Z | Z | Z |
| D (4,1) | - | X | X | X | X |
From 3,
Vendor Y had contracts in 2010 and 2019
and in 2010 D and C hasn't got any contract
and A has already got 2 different contracts from two different vendors
=> Y has a contract from B in 2010
=> B hasn't got any contracts in 2017, 2018, 2019.
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | X | X | X,W | - | - | - | - | - | - | - |
| B (7,1) | Z, Y | Z | Z | Z | Z | Z | Z | - | - | - |
| C (3,1) | - | - | W | - | - | - | - | Z | Z | Z |
| D (4,1) | - | - | X | X | X | X | - | - | - | Y |
For Y the only possible contract will be from D
=> D has got no contracts in the years 2011, 2016, 2017, 2018.
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | |
|---|---|---|---|---|---|---|---|---|---|---|
| A (3,1) | X | X | X,W | - | - | - | - | - | - | - |
| B (7,1) | Z, Y | Z | Z | Z | Z | Z | Z | - | - | - |
| C (3,1) | - | - | W | - | - | - | - | Z | Z | Z |
| D (4,1) | - | - | X | X | X | X | - | - | - | Y |
D had a contract with Y in 2019