There are 12 children in front of a zoo. Susi is the 7th from the front and Kim is the 2nd from the back. How many children are there between Susi and Kim?
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Answer: B — 3
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Hint 1 of 2
Find Susi's and Kim's spots in the line first, counting from the same end.
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Hint 2 of 2
Once you know both positions, count only the children strictly in between them.
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Approach: place both children by position, then count the gap
Counting from the front, Susi is in spot 7.
Kim is 2nd from the back of 12, so Kim is in spot 11.
The children between them sit in spots 8, 9 and 10.
Five equally big square pieces of card are placed on a table on top of each other, making the picture shown. The cards are collected up from top to bottom. In which order are they collected?
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Answer: E — 5-2-3-1-4
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Hint 1 of 2
The card on top is the one whose whole shape is fully visible, none of it hidden.
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Hint 2 of 2
Pick up the fully-showing card first, then the next one that becomes fully visible, and so on.
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Approach: peel cards top-down, taking the fully-visible one each time
The card that is completely visible (nothing covering it) is on top, so it comes off first.
Remove it, then find the next card that is now fully uncovered, and take that one.
Repeating this gives the order of collection from top to bottom.
There are two kinds of camels: bactrian camels that have 2 humps, and dromedaries that have 1 hump. Exactly 10 camels live in a certain zoo. Together they have 14 humps. How many bactrian camels are there in this zoo?
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Answer: D — 4
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Hint 1 of 2
If all 10 camels had just 1 hump, how many humps would that be?
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Hint 2 of 2
Every bactrian camel adds one extra hump beyond that; the extra humps tell you the count.
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Approach: start from all one-hump and add the extra humps
If all 10 camels had 1 hump each, that would be 10 humps.
There are 14 humps, so there are 4 extra humps.
Each bactrian camel has one extra hump, so there are 4 bactrian camels.
The picture shows a mouse and a piece of cheese. The mouse is only allowed to move to the neighbouring fields in the direction of the arrows. How many paths are there from the mouse to the cheese?
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Answer: E — 6
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Hint 1 of 2
The arrows only let the mouse go forward toward the cheese, never back.
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Hint 2 of 2
Trace one path with your finger, then carefully find every different way without repeating one.
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Approach: trace every allowed path one at a time and count them
Put your finger on the mouse and follow the arrows toward the cheese.
Each time you reach a spot with two arrows, you can pick a different way to go.
Carefully trace each different route all the way to the cheese without repeating one.
Counting all the different routes gives 6, so the answer is E.
The giants Tim and Tom build a sandcastle and decorate it with a flag. They push half the flagpole into the highest point of the sandcastle. The highest point of the flagpole is now 16 m above the floor, and the lowest is 6 m (see diagram). How high is the sandcastle?
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Answer: A — 11 m
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Hint 1 of 2
Find the whole length of the flagpole from its top and bottom heights.
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Hint 2 of 2
Half the pole is buried, so the sand reaches halfway up the pole; that halfway height is the castle.
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Approach: find pole length, then take the midpoint where the sand reaches
The pole's top is 16 m up and its bottom is 6 m up, so the pole is 16 − 6 = 10 m long.
Half the pole (5 m) is buried in the castle, starting from its bottom at 6 m.
So the sand reaches up to 6 + 5 = 11 m, which is the top of the castle.
There are white, grey and black squares. Three children use these to make this pattern. First Anni replaces all black squares with white squares. Then Bob replaces all grey squares with black squares. Finally Chris replaces all white squares with grey squares. Which picture have the three children now created?
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Answer: A
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Hint 1 of 2
Do the three colour changes one at a time, in the order Anni, then Bob, then Chris.
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Hint 2 of 2
Follow just one square of each starting colour all the way through to see what it turns into.
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Approach: follow each starting colour through the three changes in order
A black square turns white (Anni), then that white turns grey (Chris), so black ends grey.
A grey square turns black (Bob) and stays black, so grey ends black.
A white square is only changed by Chris, turning grey, so white ends grey.
Recolouring every square this way gives the picture in option A.
Together the three squirrels Anni, Asia and Elli have 10 nuts. Each one has a different number of nuts, but at least 2 nuts. Anni has the least number of nuts. Asia has the most nuts. How many nuts does Elli have?
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Answer: C — 3
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Hint 1 of 2
Anni has the fewest and each squirrel has at least 2, so start Anni as low as allowed.
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Hint 2 of 2
Try the smallest possible numbers that are all different and add to 10, then read Elli's amount.
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Approach: use the smallest distinct amounts that sum to 10
All three numbers are different, each at least 2, and they add to 10.
Anni has the fewest, so try Anni = 2; then Elli and Asia must add to 8 with Asia largest.
The only way is Elli = 3 and Asia = 5 (all different, Asia most).
