FREE CHALLENGE / Number reasoning
The Counterweight
Three small objects sit beside the luggage scale: a brass key, a metal tag and a round token. The scale is accurate, and identical objects always weigh the same.
The rules
All measurements are in grams. Each object has a positive whole-number weight. Use all three measurements to find the weight of one key.
- 34 g
- Two keys + one tag weigh 34 grams.
- 13 g
- One key + one token weigh 13 grams.
- Tag = 3 tokens
- One tag weighs the same as three tokens.
How many grams does one key weigh?
A nudge, only if you need one
Hint 1
Replace the tag in the first measurement with three tokens. You now have two keys and three tokens weighing 34 grams.
Hint 2
Two copies of the second measurement give two keys and two tokens weighing 26 grams. What is left when you compare this with 34?
Reveal the answer and reasoning
5 grams
- A tag equals three tokens, so the first measurement becomes two keys plus three tokens = 34 grams.
- Doubling the second measurement gives two keys plus two tokens = 26 grams. The extra token therefore weighs 34 − 26 = 8 grams.
- One key plus one token is 13 grams, so one key weighs 13 − 8 = 5 grams. The tag is 24 grams. Check: 2 × 5 + 24 = 34.
This is an original, standalone Launchroom challenge. It is separate from the six puzzles in the paid game. Play here, or print this page with the answer closed.
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