Puzzles of the Week (2)

First of all, thanks for all your responses. This category seems to race through the LP2I website. Many thanks to Alarick Broussaudier who has been the first to answer almost all puzzles. Théo Guillon was not far behind and thanks also to the TS’s students that might have gave a hand. You will be able to see the answers to those problems at the end of this post. But let’s go on with new puzzles !

Puzzle 4 :

« A multiple of eleven I be,
Not odd, but even you see ;
My digits (a pair),
When multiplied there,
Make a cube and a square out of me.

Determine the number. »

Puzzle 5 :

« How many segments have endpoints that are vertices of a given cube ? »

Puzzle 6 :

« Six horses eat six bales of hay in six hours. At the same rate, how long will three bales of hay last three horses ? »

And, as those three puzzles are "quite easy", here is a last one for the most experienced...

Puzzle Bonus

What is the sum of the 2010th row in the table below ?


2 + 3

4 + 5 + 6

7 + 8 + 9 + 10


Answers to PW (1) :

Puzzle 1 - Partially solved by Alarick Broussaudier (and Mrs David !) :
64 possibilities.
The second tallest player must be adjacent to the tallest player (either side). The third tallest player must be adjacent to the first two, and so on... Thus, the players can line up in 2^6 = 64 different ways (if left to right is consider different from the same order right to left).

Puzzle 2 - Solved by Théo Guillon and Alarick Broussaudier with a "TS help" :
If "abba" is the palindrome number (hum, abba’s everywhere...), then "abba" = 1000a + 100b + 10b + a = 1001a + 110b = 11*(91a + 10b) which is divisible by 11.

Puzzle 3 - Partially solved by Alarick Broussaudier :
No. Two pairs are possible, C = 160°, F = 320° and C = -24.6°, F = -12.3°. Those are not comfortable temperature ! (If you don’t see how to get the solution, come and ask a Seconde’s student, he knows the linear function that links F and C...)