Can you explain all six readings?
Four boxes were counted in pairs. Every reading can be wrong by up to 17. Find possible contents of the boxes.
The clock starts when you reveal the puzzle.SIX READINGS. ONE FAULTY MACHINE.
Trust the pattern.
Question the readings.
A little error.
A precise conclusion.
THE FOUR BOXES · YOUR PROPOSAL
YOUR TOTAL—
SIX READINGS · EACH ±17
No pair labels were recorded.Enter a count for each box. The six real pair sums will be matched to the readings.AT YOUR OWN PACE
A brain snack, with room to think.
THE ANSWER OPENS ANOTHER DOOR
Now for the lovely part.
You have an answer. Explore how it works, then take the idea somewhere new.
See why it works ↓Keep your time
THE IDEA BEHIND YOUR ANSWER
Uncertain readings.
A certain total.
Inspect how your four counts explain the six measurements. Then combine the error ranges to pin down the total.
| Pair | Your sum | Reading | Difference |
|---|
This is one legal matching. The machine’s original pair labels were lost; we do not claim to recover its actual measuring order.
PAIR THE SMALLEST WITH THE LARGEST
Three ways to count every box once.
Sort the six true pair sums. The smallest plus the largest equals the total of all four boxes. So do the second-smallest plus second-largest, and the two middle sums.
For ordered box counts a ≤ b ≤ c ≤ d, the outer sums pair (a+b) with (c+d), then (a+c) with (b+d). The middle two are (a+d) and (b+c), in either order.
Sorted true sums can be matched to sorted readings: if two matching lines cross, uncrossing them keeps both errors within the same tolerance. This gives one valid matching without guessing the lost labels.
43 + 255 ± 34 → 264 to 332
99 + 233 ± 34 → 298 to 366
123 + 141 ± 34 → 230 to 298
The total must lie inside all three ranges. Their only common value is 298. Your box contents prove that this value can actually occur.
The total is fixed, even though the individual contents need not be. As a further challenge, try to find another set of four counts.
The idea to take away
Uncertainty can become precise when several independent constraints overlap. Preserve the error ranges instead of treating each noisy reading as exact.