The tactics behind the ticket: A Critical Line puzzle solution

Find out the solution!

The lottery ticket I found incorporated a series of operations that were challenging to decipher, so well done to those who managed to untangle the clues and put together a solution.

The transformation from name to entry worked as follows:

1. Count the total number of letters in the first and last name and put this value in brackets on the right
2. Take the first 6 letters of the first and last name
3. Translate from alphabet characters to numbers 1 through 26 where A=1, B=2, … Z=26 (often referred to as A1Z26 substitution cypher)
4. Convert these 6 numbers from base 10 to the base of the number in brackets for that entry
5. Order these numbers from smallest to largest

There were a few clues to help you get there:

• Scanning the QR code yields “TICKETNUMBERSORDERED” – a double clue about the presentation of the entries on the ticket as well as the order within each entry
• The presence of 1A in entry 4 suggests bases other than base 10 might be involved
• Generally, the entry numbers are larger (viewed in base 10) where the bracketed number is smaller

Without further a-clue, let’s get into the answers!

a) Which well-known Australian actuary does each entry relate to?

‘Well-known Australian actuaries’ leads you towards the Actuary of the Year winners page published by the Institute. You can confirm that you have the right people if you recognise that the number of letters in the most recent six winners’ names matches with the number in brackets. The QR clue TICKETNUMBERSORDERED applies here because the names are in order from the most recent (as of puzzle publication) backwards.

The final answer to this component is, in order down the ticket, Sam Zheng, Iris Lun, Jan Swinhoe, Rade Musulin, Sharanjit Paddam, and Chris Dolman.

For the next two answers a conversion table is useful:

b) What was obscured in entry 5?

The answer here relates to the N in SHARANJIT. Translated to A1Z26 yields 14, which is E in base 15.

c) Why entries 2 and 5 are not like the others?

The conversion rules above have two issues – IRIS and SHARANJIT have duplicated characters. The value associated with the second instance of these characters is incremented by one to ensure the lottery numbers chosen for each entry are unique.

d) What the entry for your name (or pseudonym) would be?

This answer depends on you! The only requirement is that your name/pseudonym is at least 6 characters in length.

This month’s lottery logicians

Well done to everyone who made headway on this puzzle; it was particularly challenging! We received one correct answer to all four questions from two punters this issue:

• AIrtful Dodger
• Nicholas Lourensz

Nicholas Lourensz was randomly selected and won the prize of a $50 voucher from the Actuaries Institute.

Until next time!