IKMC 2027 - Grades 5-6 - Self-study SET 6 - Thematic Batch 3

On the day immediately after Sam’s birthday, she says, “The day after tomorrow is Thursday.” On which day was her birthday?

International Children’s Day, 1 June 2021, was a Tuesday. Alice turns 20 on 6 September 2021. What day of the week is that?

A rabbit hutch has 22 cells arranged as shown. Each cell contains a rabbit or shares an edge with a cell containing a rabbit. What is the smallest possible number of rabbits?



Editorial interpretation: The source’s awkward edge wording means every cell contains a rabbit or shares an edge with a rabbit’s cell, as in the source solution.

Emily fills the triangular grid so that any two cells sharing a side have the same fixed sum. Two numbers are already given. What is the total of all the numbers after she finishes?

The square grids are decorated according to the pattern shown. How many unit cells will be shaded in figure 11?



Editorial convention: Continue by increasing each grid side by one and shading both diagonals.

Which of the figures below necessarily consists of more than two pieces of string?



Original source choices (retained):

A. I, III, IV, V

B. II, III, IV

C. I, III, V

D. All five figures

E. None of them

Source consistency task: Preserve and inspect the original question and choices above. Count the closed strands in each figure, decide which satisfy the literal condition “more than two”, and explain the discrepancy with source key C. This is an essay; no incorrect source choice is auto-scored.

The solid is made of 1×1×1 cubes. Tom wants a rectangular cardboard box that contains the entire solid. What are the smallest dimensions?



Editorial convention: The box edges are parallel to the unit-cube edges.

Kenny has the six pieces shown. Which three can be fitted together to form a square?



Source solution convention: Pieces may be rotated and flipped.

On Sunday morning Alex sends a photo to five friends. The next day each shares it with two new people. Thereafter everyone who received it the previous day shares it with two new people, and nobody receives it twice. What is the first day on which more than 100 people in total have seen the photo?

A cricket enclosure has 12 cells, with six crickets initially occupying the cells shown on the left side of the stepped boundary. How many jumps in total are needed, at minimum, to move them to the six initially empty cells? A jump passes over one cell horizontally, vertically or diagonally and lands in an empty cell.



Clarification: The six occupied cells and six targets are separated by a stepped boundary, not a straight middle line. Every jump skips exactly one intervening cell.

Four flowers have 4,5 or 6 petals. Five-petalled flowers always lie; four- and six-petalled flowers always tell the truth. Red claims their total is 17, orange 18, yellow 21 and pink 22. Exactly one tells the truth. Which colour is it?

King Lý Thái Tổ visits the families in the village shown, using each road at most once. Entering and leaving along the two marked arrows, what is the greatest number of families he can visit?



Editorial convention needed for source answer 13: Enter at the lower arrow and leave at the upper arrow, without reusing any road. Stopping inside instead would permit all 14 families.

Three cards each bear a three-digit number, and their total is 826. Two digits are hidden by the overlap shown. What is the sum of the hidden digits?

Linas has 32 black and 32 white unit cubes and builds a 4×4×4 cube. He maximises the white portion of its exterior surface. What fraction of that surface can be white?

Clown Dave stands on two balls and a cube as shown. The lower ball has radius 6 dm, three times the upper ball’s radius. The cube’s edge is 4 dm longer than the smaller radius. How high above the ground are Dave’s feet?

Tom lists all four-digit numbers made from the digits 0,1,1,2 in increasing order. What is the difference between the two neighbours of 2011 in this list?

The first 100 positive integers are concatenated to form 1234567891011…99100. How many digits 1 occur?

How many pairwise different angle measures can be selected from the diagram?



Editorial convention: Count non-reflex angles between the drawn rays.

The consecutive positive integers are placed in the four rows following the displayed pattern. In which row will 2017 appear?



Editorial convention: Continue the displayed repeating block of ten row positions.

Three boxes are white, red and blue. One contains chocolate, one apples and one is empty. Chocolate is in the white or red box; apples are in neither the white nor blue box. Which contains chocolate?