1.
Four donors — W, X, Y, and Z — gave marrow samples. X gave more than W. Y gave less than W. Z gave more than X. List all four from most to least.
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Did you know? Donors are matched to patients by markers on their cells. A brother or sister is the most likely match, but even then it is only about one chance in four.
2.
Three technicians — Amina, Idris, and Khadija — each work one bench: stem cells, platelets, or plasma. Amina does not work platelets. Idris works plasma. Who works each bench?
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Did you know? Plasma is the pale gold liquid left when you take the cells out of blood. It is more than half of what is in your veins.
3.
A dish starts with 3 stem cells at 9:00. The number doubles every 30 minutes. How many cells are in the dish at 11:00?
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Did you know? Stem cells are the only cells that can copy themselves forever and still turn into something else later. That is what makes them so useful.
4.
Trays are numbered 1 to 20. Every 4th tray gets a red label. Every 5th tray gets a blue label. Which tray gets both labels? And how many trays get no label at all?
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Did you know? Every sample in a real lab is labelled twice and scanned. A single mixed-up tray could send the wrong marrow to the wrong patient.
1.
Four technicians — Amina, Bilal, Hafsa, and Idris — each tested one sample: red cells, white cells, platelets, or plasma. Amina tested neither plasma nor platelets. Bilal tested white cells. Hafsa did not test plasma. Who tested what?
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Did you know? A single drop of blood holds about five million red cells, seven thousand white cells, and a quarter of a million platelets.
2.
Three sealed sample boxes look identical, but one is heavier than the other two. You have a balance scale. What is the fewest number of weighings that is guaranteed to find the heavy box? Explain why it always works.
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Did you know? A balance scale does not tell you a weight. It only tells you which side is heavier — and that turns out to be enough to solve a great many puzzles.
3.
A machine produced 2 cells, then 6, then 18, then 54. What comes next, and what is the rule?
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Did you know? Growth that multiplies instead of adding is called exponential. It starts slowly and then runs away — which is exactly how an infection can get ahead of you.
4.
A sample must be checked every 15 minutes, starting at 8:00 and finishing at 10:00, with a check at both the start and the finish. How many checks are made altogether?
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Did you know? Marrow samples are kept at body temperature and checked on a strict clock. Cells left too long outside those conditions stop being usable.
3rd Grade
1. Z, X, W, Y (most to least).
X > W and Y < W gives X, W, Y. Z > X puts Z on top: Z, X, W, Y. Nothing here needs a number — only the order.
2. Idris — plasma. Amina — stem cells. Khadija — platelets.
Idris is given as plasma. Amina is not platelets, and plasma is taken, so Amina is stem cells. Khadija gets what is left: platelets.
3. 48 cells.
9:00 = 3 · 9:30 = 6 · 10:00 = 12 · 10:30 = 24 · 11:00 = 48. Four doublings in two hours, not two.
4. Tray 20 gets both. 12 trays get no label.
Red: 4, 8, 12, 16, 20 (5 trays). Blue: 5, 10, 15, 20 (4 trays). Tray 20 is on both lists. Labelled at least once = 5 + 4 − 1 = 8. So 20 − 8 = 12 with no label.
4th Grade
1. Amina — red cells. Bilal — white cells. Hafsa — platelets. Idris — plasma.
Bilal is given as white. Amina is not plasma, not platelets, and white is taken, so Amina is red cells. Hafsa is not plasma, and white and red are taken, so Hafsa is platelets. Idris takes the last one: plasma. A grid of four names by four samples, crossing off, is the clean way to show it.
2. One weighing.
Put one box on each pan and keep the third aside. If one side sinks, that is the heavy box. If they balance, the heavy one is the box you set aside. Either result identifies it, so one weighing always suffices. The answer is not "two" — the balanced case is what does the work.
3. 162. The rule is × 3.
2 → 6 → 18 → 54, each three times the one before. 54 × 3 = 162. The gaps (4, 12, 36) are not constant, which rules out adding.
4. 9 checks.
8:00 to 10:00 is 120 minutes. 120 ÷ 15 = 8 gaps — but a check sits at both ends of every gap, so the count of checks is 8 + 1 = 9. Write them: 8:00, 8:15, 8:30, 8:45, 9:00, 9:15, 9:30, 9:45, 10:00.