The solution to the matchstick puzzle
Move the lower right vertical matchstick of the number 3 to the lower left side of the same number.
This transforms the number into:
731
the new number:
721
The equation is clear:
721 is smaller than 731.
All the conditions of the task are thus fulfilled. Exactly one matchstick was moved, all three digits are still clearly recognizable, and the value of the new number is lower than the original value.
This is how the middle digit changes
The original 3 has a horizontal line at the top, in the middle, and at the bottom. Additionally, there are two vertical lines on the right. To create the shape of a 2, the upper right vertical line is still needed. However, the lower vertical line must be on the left instead of the right.
That’s precisely why only one movement is required. The lower right matchstick is not removed or set aside, but immediately moved to the lower left position. The existing horizontal pieces of wood then form a clearly recognizable second piece together with the two vertical pieces of wood.
The tens digit 3 thus becomes the smaller tens digit 2. The value of the entire number decreases by ten as a result.
731 − 10 = 721
Why 721 is the right answer
The hundreds place remains unchanged at 7. Therefore, only the tens and units places need to be compared. In 731, the tens place is 3, while in 721 it is 2.
Since 2 is less than 3, the entire number 721 is automatically less than 731. The last digit plays no further role in this comparison because it remains the same in both numbers.
The solution is particularly elegant because the matchstick is moved within the same digit. It doesn’t need to be moved to either the 7 or the 1. This keeps the arrangement clear and the new number is immediately readable.
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