1.
6 researchers meet at the bench. Every researcher shakes hands with every other researcher exactly once. How many handshakes happen altogether?
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Answer:
Did you know? Your body's defences learn. The second time a germ shows up, the answer to it is faster and stronger than the first.
2.
On a balance, 3 vials exactly balance 1 flask. A flask and a vial together weigh 32 grams. How much does one vial weigh? How much does the flask weigh?
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Answer:
Did you know? A neutrophil, the commonest white blood cell, lives less than a day once it leaves the blood.
3.
A test starts at 9:45 am. It runs for 50 minutes, then cools down for 25 minutes, then is scanned for 40 minutes. At what time is it finished?
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Answer:
Did you know? Much of your immune repair happens while you sleep, which is one reason being ill makes you so tired.
4.
A dish of bacteria doubles every day. On day 12 the dish is completely full. On which day was it half full? And on which day was it a quarter full? Careful — this one is not half of 12.
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Answer:
Did you know? In good conditions some bacteria can double in number about every twenty minutes.
1.
Three lab technicians — Yusra, Bilal, and Amina — each run a different test (blood, swab, culture) on a different shift (morning, evening, night). Who runs what, and when?
1. The culture test is run on the night shift. 2. Bilal runs the culture test. 3. Yusra does not work the morning shift. 4. The blood test is run on the morning shift.
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Answer:
Did you know? The spleen filters blood and holds a reserve of white blood cells, ready to be released.
2.
A scanner holds only 2 slides at a time. Every slide must be scanned on both of its sides, and each scan takes 5 minutes. What is the shortest time to finish 3 slides? It is less than you think.
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Answer:
Did you know? Antiseptic on a cut kills germs — but it kills some of your own repairing cells too, which is why clean water is often enough.
3.
A box holds vials of 4 different vaccines, all mixed together and all looking identical. Without looking, what is the fewest vials you must pick to be certain you have 3 of the same kind?
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Answer:
Did you know? Identical twins can accept each other's organs without rejection — their immune systems read them as the same person.
4.
A tray of samples is sorted. Half of them go to the North lab. Then 3 are set aside for retesting. Then half of what is left goes to the South lab, and 7 samples remain on the tray. How many samples were on the tray to start with?
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Answer:
Did you know? Breast milk carries the mother's antibodies, so a baby borrows a defence while building its own.
3rd Grade
1. 15 handshakes.
Each of the 6 shakes 5 hands = 30 — but that counts every handshake twice, once from each side. So 30 ÷ 2 = 15. Or count down the line: 5 + 4 + 3 + 2 + 1 = 15.
2. A vial is 8 g; the flask is 24 g.
Swap the flask for what it balances: a flask is 3 vials, so "flask + vial" is 4 vials = 32 g. One vial = 32 ÷ 4 = 8 g; flask = 3 × 8 = 24 g. Check: 24 + 8 = 32. ✓
3. 11:40 am.
One stage at a time: 9:45 + 50 → 10:35; + 25 → 11:00; + 40 → 11:40 am. Adding 115 minutes first also works — if you know that is 1 h 55, not 1 h 15.
4. Half full on day 11; a quarter full on day 10.
Run it backwards: doubling forwards is halving backwards. The day before full it was half full — day 11 — and one more back, day 10. Day 6 is the expected wrong answer; the last day adds as much as every day before it put together.
4th Grade
1. Bilal — culture — night · Yusra — swab — evening · Amina — blood — morning.
Clue 2 gives Bilal the culture; clue 1 puts him on night. Clue 3 keeps Yusra off the morning and night is taken, so Yusra is evening, leaving Amina the morning. Clue 4 makes morning the blood test → Amina blood, Yusra swab. Without clue 4 those two could swap.
2. 15 minutes.
Slides A, B, C. Round 1: A-front, B-front. Round 2: A-back, C-front — this is the move; B comes off half done on purpose. Round 3: B-back, C-back. 3 × 5 = 15 minutes. The 20-minute trap finishes A and B first, then runs C alone with the scanner half empty.
3. 9 vials.
Ask what the unluckiest run looks like: 2 of every kind — 4 × 2 = 8 — and still no set of three. There are only 4 kinds, so vial 9 must be a third of something. 9. "Certain" means it holds on your worst day.
4. 34 samples.
Work backwards, flipping every step. 7 left after half went south → 14. Undo the 3 set aside → 17. That was what remained after half went north, so double it → 34. Forwards: 34 → 17 → 17 − 3 = 14 → 7. ✓