Reasoning
Since no digit is duplicated, neither number can end in 1, otherwise, the last digit of the answer would already have been used.
Neither number can end in 5 because the answer would then end in 5 or 0.
So the first number can only be 62, 63, 64, 67, or 68.
We can now look at what the second number can end with, and we find that …
if the first number was 62, the second number can only end in 4 or 7.
Why …
not 1 as previously explained
not 2 because we've already used that in the 62
not 3 because 62 x *3 would end in 6, which is already in the 62
not 5 as previously explained
not 6 because we've already used that in the 62
not 8 because 62 x *8 would end in 6, which is already in the 62
We can repeat this for the other possible first numbers and find that …
if the first number was 62, the second number can only end in 4 or 7.
if the first number was 63, the second number can only end in 4, 7, or 8.
if the first number was 64, the second number can only end in 2, 3, 7, or 8.
if the first number was 67, the second number can only end in 2, 3, or 4.
if the first number was 68, the second number can only end in 3 or 4.
Let's check these in turn …
If the first number was 62, the only possible values are:
62 x 14 = 868
62 x 34 = 2108
62 x 54 = 3348
62 x 74 = 4588
or
62 x 17 = 1054
62 x 37 = 2294
62 x 57 = 3534
62 x 87 = 5394
Only 4 calculations are required for each option, as we didn't need to check 62 x 84 as we already know that the answer would end in 8, or 62 x 47 as we already know that the answer would end in 4.
All of these answers fail as they don't contain all of the digits.
Similarly, we can look at 63, then 64, etc. For each of the numbers, we have to check the possible endings, but in each case, only 4 calculations are required (as seen in the examples above).
We (quickly?) find 64 x 58 = 3712.
?
Puzzle 154
Alex can eat 27 chocolates in an hour, Billie can eat 2 chocolates in 10 minutes, and Charlie can eat 7 chocolates in 20 minutes.
How long will it take them to share and eat a large box of 120 chocolates while watching a movie?
Hint
How many chocolates can they eat in one hour?
Answer
2 hours.
Reasoning
In one hour, Alex eats 27 chocolates, Billie eats 12, and Charlie eats 21.
A total of 60 chocolates.
Therefore, 120 chocolates would take 2 hours.
??
Puzzle 155
These five business people represented different companies at a recent trade fair. Unfortunately, the hotel they were all due to stay in had accidentally double booked their rooms. They tried other hotels in the area but all were fully booked. Consequently, they all agreed to share the only two rooms available in the hotel, one twin and one triple.
From the clues, can you work out each person's name, company and official title?
When the five realised their dilemma, they drew straws to see who would share with whom. The outcome for four of them was that the CEO shared with the business person from ABM Inc. and Glenn shared with the Developer. Alex does not work for Reed Right and is not the Director. The Director does not work for Lantel or Blue Teeth. Neither Clarkson nor Grimaldi works for Reed Right. Grimaldi is either the IT Analyst or the CEO. The business person from Reed Right did not share a room with Taylor. Clarkson, who does not work for Lantel, shared with either Taylor or Grimaldi but not both. Glenn's surname is either Casson or Graves. Glenn did not share with Charlie. The business person from Chiptech shared with the business person from Lantel. The CEO shared with the IT Analyst. Casson works for either Blue Teeth or Chiptech. Neither Jesse nor Alex works for ABM Inc. Fielder shared with the Director. The business person from Blue Teeth shared with the Developer.
First names : Alex, Charlie, Glenn, Jesse, Taylor.
Last names : Casson, Clarkson, Fielder, Graves, Grimaldi.
Company : ABM Inc., Blue Teeth, Chiptech, Lantel, Reed Right.
Position : Accountant, CEO, Developer, Director, IT Analyst.
Answer First Last Name Company Position Charlie Grimaldi ABM Inc. IT Analyst Glenn Casson Chiptech Director Jesse Graves Reed Right CEO Alex Clarkson Blue Teeth Accountant Taylor Fielder Lantel Developer
To solve this puzzle, you first need to determine who shared which room with whom. Three delegates shared the triple and two shared the twin. The CEO shared with the business person from ABM in one room and Glenn shared with the Developer in the other (1). Since Grimaldi is either the IT Analyst or the CEO (3) and the CEO shared with the IT Analyst, Grimaldi is in the same room as whoever is the CEO, IT Analyst and ABM delegate although Grimaldi could have been one of these people. Glenn did not share with Charlie (6) so Charlie is in the same bedroom as, and possibly is, the CEO, IT Analyst, Grimaldi and/or the ABM delegate. Grimaldi and Taylor were in different rooms so Taylor shared a room with Clarkson (5) and the Reed Right delegate was in a different room to Taylor. At this stage we know:
Room 1
CEO
IT Analyst
ABM delegate
Grimaldi
Charlie
Reed Right delegate
Room 2
Glenn
Developer
Taylor
Clarkson
Since the Chiptech delegate shared with the Lantel delegate (7), both of these must have been in room 2 otherwise there would be four delegates in room 1 which is not possible.
Now this has been ascertained, the puzzle can be solved:
The CEO shared with the IT Analyst so the IT Analyst must work for ABM (Clues 1 and 8) so the CEO must work for Reed Right. Since Grimaldi does not work for Reed Right, they must be the IT Analyst. Clarkson, Fielder and Casson are in room 2 so the CEO must be Graves. Graves is not Glenn (1), Taylor (4), Charlie (IT Analyst) or Alex (2) so must be Jesse. Clarkson is not Taylor (5), Glenn (6), Charlie or Jesse (in room 1) so must be Alex. The Director does not work for Lantel or Blue Teeth (2), Reed Right or ABM (room 1) so must work for Chiptech. This is not Graves or Grimaldi (room 1), Clarkson (2) or Fielder (11) so must be Casson. Since Graves' first name is Jesse, Casson must be Glenn (6). Alex Clarkson does not work for Reed Right or ABM (room 1), Lantel (5) or Chiptech so must work for Blue Teeth. Since they are not the Developer (12) they must be the Accountant. This leaves Taylor Fielder who is the Developer for Lantel.
Santa always leaves plans for his elves to determine the order in which the reindeer will pull his sleigh. This year, for the European leg of his journey, his elves are working to the following schedule, that will form a single line of nine reindeer:
Comet behind Rudolph, Prancer and Cupid. Blitzen behind Cupid and in front of Donder, Vixen and Dancer. Cupid in front of Comet, Blitzen and Vixen. Donder behind Vixen, Dasher and Prancer. Rudolph behind Prancer and in front of Donder, Dancer and Dasher. Vixen in front of Dancer and Comet. Dancer behind Donder, Rudolph and Blitzen. Prancer in front of Cupid, Donder and Blitzen. Dasher behind Prancer and in front of Vixen, Dancer and Blitzen. Donder behind Comet and Cupid. Cupid in front of Rudolph and Dancer. Vixen behind Rudolph, Prancer and Dasher.
Can you help the elves work out the order of the reindeer?
