Problem K/C. 737. (October 2022)

K/C. 737. Given two threads of known length, we can measure and mark off the sum or difference of their lengths, and also the half length of a thread by folding it into two. We are given two threads of length 2240 cm and 1760 cm. Describe a procedure to mark off a length of 10 cm by using a single measurement (that is, measuring the sum or difference of lengths is allowed only once, but halving a length by folding can be performed many times).

(5 pont)

Deadline expired on November 10, 2022.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Például a 2240 cm-es zsinórt ötször elfelezve 70 cm hosszú zsinórt kapunk, míg az 1760 cm hosszú zsinórt 4-szer elfelezve 110 cm hosszú zsinórt kapunk. A 110 cm és 70 cm hosszú zsinórok különbsége 40 cm, amit kétszer elfelezve 10 cm hosszú zsinórt kapunk, mellyel kimérhetjük a 10 cm-es távolságot.

Statistics:

321 students sent a solution.
5 points:	265 students.
4 points:	3 students.
3 points:	2 students.
2 points:	4 students.
1 point:	1 student.
Unfair, not evaluated:	28 solutionss.
Not shown because of missing birth date or parental permission:	13 solutions.

Problems in Mathematics of KöMaL, October 2022