SOF IMO case studies
SOF IMO · Put your knowledge to work in context.
The SOF International Mathematics Olympiad (IMO) is an annual school-based mathematics competition run by the Science Olympiad Foundation (SOF) for students in classes 1 to 12. It is aimed at students enrolled in a school recognised by SOF, and it is designed to assess mathematical reasoning and logical ability rather than rote recall. The SOF IMO case studies are 5 cases and about 3,167 words.
1The Greenwood School Shift Cipher: Rule, Red Herring and Reverse-Decoding
The Cryptography Club at Greenwood School has invented a shift cipher of its own. To encode a word, move its first letter 1 place forward in the alphabet, its second letter 2 places forward, its third 3 places forward, and so on, where the shift equals the letter's position inside the word.
601 words, about 3 min2The Assembly Hall Clock That Gains Four Minutes Every Hour
Xavier's assembly hall clock runs fast. In every 60 minutes of real time it advances 64 minutes, so it gains exactly 4 minutes per real hour, steadily and without jolts.
551 words, about 3 min3Digit Detective: A Three-Digit Card With One Condition Too Many?
The 'Digit Detective' round at a school olympiad hands Team Asha a sealed card. The card states five conditions about a hidden number: it is three-digit; its three digits are all different and none of them is zero; the digits add up to 12; the number exceeds its own reversal by 297; and the hundreds digit is even.
723 words, about 4 min4One Truth Only: Four Boxes, Four Inscriptions, One Medal
The maths fair at Nalanda School has a stall called 'One Truth Only'. Four identical steel boxes, numbered 1 to 4, sit on a table.
680 words, about 3 min5The Hall Robot: Counting Shortest Routes Around a Pillar
A floor-cleaning robot works in a square hall marked with a 5 × 5 grid of junction points, with coordinates from (0, 0) at the south-west corner to (4, 4) at the north-east corner. The robot starts at (0, 0) and must reach (4, 4).
612 words, about 3 min