At first glance, this matchstick puzzle seems surprisingly simple: You are given the number 731 , and you may move exactly one matchstick. The goal is to then obtain a number that is less than 731.
The task is:
Make a number smaller than 731. To do this, move only one matchstick.
What initially appears to be a simple math problem is actually a test of attention, spatial reasoning, and the ability to view familiar shapes from a different perspective. Simply removing any matchstick isn’t enough. The selected matchstick must be placed elsewhere, and the final result should still be a clearly recognizable number.
Take a close look at the number.
The number consists of the three digits 7, 3, and 1. Each of these digits was made up of several matchsticks. To find the solution, it’s worth not moving a matchstick immediately, but first looking at each digit individually.
- The 7 is located in the hundreds place and therefore has the greatest influence on the value of the number.
- The 3 is in the tens place and can be converted into another digit with a small change.
- The 1 is located in the ones place and consists of only a vertical matchstick.
One obvious idea would be to change the 7. Since it’s in the first position, a smaller hundreds digit could significantly reduce the overall value. However, with the depicted shape of the 7, there are only a few ways to remove a matchstick while still leaving a clearly legible digit.
The number 1 also immediately stands out because it consists of only a single matchstick. However, if this matchstick is removed, the digit disappears completely. Furthermore, it would have to be inserted elsewhere in such a way that the remaining shapes still form a correct number. This approach therefore does not readily lead to a convincing solution.
The crucial clue is in the middle. The number 3 consists of three horizontal and two vertical matchsticks. By moving one of the vertical matchsticks, a different valid number can be formed.
Why the puzzle seems more difficult than it actually is
Many observers initially focus on the number 731 as a whole. They try to mentally form different numbers or are determined to make the first digit smaller. This very way of thinking makes the task more complicated.
It is more helpful to consider the number not as a fixed mathematical object, but as a collection of individual lines. Each line can change its position. The question, therefore, is not only which matchstick can be removed, but above all, which new digit results from this shift.
Three conditions must be met simultaneously when searching for the solution:
- Only one matchstick may be moved.
- After the change, legible digits must remain.
- The newly generated number must be less than 731.
It is therefore not enough to simply change the number visually. The result must also be mathematically correct. A number like 751, for example, would still be valid, but it would be larger than 731 and therefore would not solve the problem.
Focus on the number 3
Pay particular attention to the lower vertical matchstick on the right side of the 3. If this matchstick is removed, the original 3 is initially no longer complete. However, this exact matchstick can be reinserted on the opposite side.
Instead of leaving it in the bottom right corner, it is moved to the bottom left. The three horizontal matchsticks remain unchanged. The upper vertical piece of wood on the right side also remains in its position.
This single movement changes the middle digit. The 3 becomes a 2. The first digit, 7, and the last digit, 1, remain completely unchanged.
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